restart;simpson_n := proc(f,a,b,e) local df4, res; df4 := eval(diff(f(x),x$4),x=a); res:=evalf(((b-a)^b*df4/(16*180*e))^(1/4)); return round(res); end proc:simpson := proc(f,a,b,e) local h, res, df4, n, sum1, sum2, j; #n:=simpson_n(f,a,b,e); n:=4; #print(n); h:=(b-a)/(n*2); sum1:=0; for j from 1 by 2 to 2*n-1 do sum1:=sum1+f(a+j*h); end do; sum2:=0; for j from 2 by 2 to 2*n-2 do sum2:=sum2+f(a+j*h); end do; res:=h/3*(f(a)+f(b)+4*sum1+2*sum2); return evalf(res); end proc:f:=(x)->sqrt(1+x^5);

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUklc3FydEc2JEkqcHJvdGVjdGVkR0YvSShfc3lzbGliR0YlNiMsJiIiIkYzKiQ5JCIiJkYzRiVGJUYl

plot(f(x),x=1..Pi);

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

a:=1;

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b:=Pi;

NiM+SSJiRzYiSSNQaUdJKnByb3RlY3RlZEdGJw==

e := 10^(-4);

NiM+SSJlRzYiIyIiIiImKysi

Int(f(x),x=a..b);

NiMtSSRJbnRHNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYkKiQsJiIiIkYsKiRJInhHRigiIiZGLCNGLCIiIy9GLjtGLEkjUGlHRiY=

approx_s:=simpson(f,a,b,e);

NiM+SSlhcHByb3hfc0c2IiQiK0tRV246ISIp

genau:=evalf(int(f(x),x=a..b));

NiM+SSZnZW5hdUc2IiQiKz9oV246ISIp

fehler_s:=abs(approx_s-genau);

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restart;simpson_mit_n := proc(f,n,a,b) local h, res, df4, sum1, sum2, j; h:=(b-a)/(n*2); df4 := eval(diff(f(x),x$4),x=a); sum1:=0; for j from 1 by 2 to 2*n-1 do sum1:=sum1+f(a+j*h); end do; sum2:=0; for j from 2 by 2 to 2*n-2 do sum2:=sum2+f(a+j*h); end do; res:=h/3*(f(a)+f(b)+4*sum1+2*sum2); #res:=h/3*(f(a)+f(b)+4*sum(f(a+j*h),j=1..2*n-1)+2*sum(f(a+j*h),j=2..2*n-2))-((b-a)*h^4)/180*df4; return evalf(res); end proc:f:=(x)->exp(2*x)/x^(2/5);

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYtSSRleHBHNiRJKnByb3RlY3RlZEdGMEkoX3N5c2xpYkdGJTYjLCQ5JCIiIyIiIkY0IyEiIyIiJkYlRiVGJQ==

j:=(x)-> piecewise( x=0, 1, x<>0, exp(2*x)-p4(x)/x^(2/5) );

NiM+SSJqRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkqcGllY2V3aXNlR0kqcHJvdGVjdGVkR0YuNiYvOSQiIiEiIiIwRjFGMiwmLUkkZXhwRzYkRi5JKF9zeXNsaWJHRiU2IywkRjEiIiNGMyomLUkjcDRHRiU2I0YxRjNGMSMhIiMiIiYhIiJGJUYlRiU=

plot(f(x),x=0..1);

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

taylor(exp(2*x), x=0, 5);

NiMrL0kieEc2IiIiIiIiISIiI0YmRihGKCMiIiUiIiRGKyNGKEYrRiotSSJPR0kqcHJvdGVjdGVkR0YvNiNGJiIiJg==

p4 := x -> 1+2*x+2*x^2+4/3*x^3+2/3*x^4;

NiM+SSNwNEc2ImYqNiNJInhHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwsIiIiRi05JCIiIyokRi5GL0YvKiRGLiIiJCMiIiVGMiokRi5GNCNGL0YyRiVGJUYl

a:=0;

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b:=1;

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n:=6;

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Int(f(x),x=a..b);

NiMtSSRJbnRHNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYkKiYtSSRleHBHRiU2IywkSSJ4R0YoIiIjIiIiRi8jISIjIiImL0YvOyIiIUYx

genau := evalf( int(f(x),x=a..b) );

NiM+SSZnZW5hdUc2IiQiK3k2YW1VISIq

approx := simpson_mit_n(j,6,0,1);

NiM+SSdhcHByb3hHNiIkIStCVyopSHohIzU=

approx := simpson_mit_n(j,6,0,1) + evalf(int(p4j(x)/x^(2/5), x=0..1));

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abs(approx-genau);

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restart;with(plots,listplot):with(plots,display):t:=(i) -> a + i*h;

NiM+SSJ0RzYiZio2I0kiaUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCZJImFHRiUiIiIqJjkkRi5JImhHRiVGLkYuRiVGJUYl

eul := proc(f, a, b, h, alpha) local i, n, w, res, t, tmp; n := (b-a)/h; w := [alpha]; t:=(i) -> a + i*h; for i from 0 to n-1 do tmp:=evalf(op(-1,w)+h*f(t(i),op(-1,w))); w:=[op(w),tmp]; #print(w); end do; return w; end proc:f:=(t,y) -> 1+y/t;

NiM+SSJmRzYiZio2JEkidEdGJUkieUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYiIiJGLiomOSVGLjkkISIiRi5GJUYlRiU=

a:=1;

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b:=2;

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alpha:=2;

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n:=20; h:=(b-a)/n;

NiM+SSJuRzYiIiM/

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m:= unapply(rhs(dsolve({diff(y(k),k)=1+y(k)/k,y(1)=2},y(k))),k);

NiM+SSJtRzYiZio2I0kia0dGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYsJi1JI2xuRzYkSSpwcm90ZWN0ZWRHRjFJKF9zeXNsaWJHRiU2IzkkIiIiIiIjRjVGNUY0RjVGJUYlRiU=

m(1.65);

NiMkIitEI3ppNyUhIio=

appr:=eul(f,a,b,h,alpha);

NiM+SSVhcHByRzYiNzciIiMkIisrKytdQCEiKiQiK180US1CRiokIitLWS5kQ0YqJCIrREEnUWgjRiokIiteSnhzRkYqJCIreFNvTEhGKiQiKyEzPWw0JEYqJCIrTlI/aEtGKiQiKy9ibkZNRiokIis2NyhlZiRGKiQiKyZlTGR3JEYqJCIraSkzcyRSRiokIitSbUM1VEYqJCIrbiYqeiVHJUYqJCIrJTNCM1klRiokIitzXkZRWUYqJCIrXGg2PFtGKiQiK3glM3QqXEYqJCIrJmY7KXleRiokIitrbmdoYEYq

exact:=[seq(evalf(m(t(j))),j=0..n)];

NiM+SSZleGFjdEc2Ijc3JCIiIyIiISQiK3MnSDc6IyEiKiQiKyk+VFtJI0YsJCIrTWlzZ0NGLCQiK29leT1FRiwkIitSJUgqeUZGLCQiK1dOMlRIRiwkIisrNzkwSkYsJCIrSjYxcktGLCQiK2Ryd1FNRiwkIitpdz4zT0YsJCIrVl5IelBGLCQiKzJlK19SRiwkIitEI3ppNyVGLCQiK0Yhbz9JJUYsJCIrSHdLeldGLCQiKygqZixlWUYsJCIrS000UVtGLCQiKyVRQSY+XUYsJCIreHNFLV9GLCQiK2hWSCdRJkYs

i:=(1.65-a)/h+1;

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op(14,appr);

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op(14,exact);

NiMkIitEI3ppNyUhIio=

pa := listplot(appr): pe := listplot(exact): display([pa,pe]);

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

fehler := map(abs,appr-exact);

NiM+SSdmZWhsZXJHNiI3NyQiIiFGKCQiKHMnSDchIiokIihZLVkjRiskIigtO3AkRiskIihWTyNcRiskIigpR2NoRiskIihuJSpRKEYrJCIoP0ppKUYrJCIoJz5kKSpGKyQiKWA7NDZGKyQiKV5rSzdGKyQiKWU6YzhGKyQiKVhwejlGKyQiKSdlS2ciRiskIilnJW9zIkYrJCIpWFhdPUYrJCIpRDN1PkYrJCIpJEd4NCNGKyQiKTJSQEFGKyQiKSNvXU0jRiskIikoZihvQ0Yr

listplot(fehler);

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

max(op(fehler));

NiMkIikoZihvQyEiKg==

i:=(1.88-a)/h+1;

NiM+SSJpRzYiJCIlZz0hIiM=

op(18,appr);

NiMkIitcaDY8WyEiKg==

op(19,appr);

NiMkIit4JTN0KlwhIio=

evalf((18-1)*h+a);

NiMkIisrKytdPSEiKg==

evalf((19-1)*h+a);

NiMkIisrKysrPiEiKg==

exakt:=m(1.88);

NiM+SSZleGFrdEc2IiQiK1Q0ellcISIq

approx:=op(18,appr)+((op(19,appr)-op(18,appr))*(1.88-1.85))/h;

NiM+SSdhcHByb3hHNiIkIitZOkJEXCEiKg==

approx:=op(18,appr)+(op(19,appr)-op(18,appr))*(3/5);

NiM+SSdhcHByb3hHNiIkIitZOkJEXCEiKg==

abs(approx-exakt);

NiMkIikmUmY6IyEiKg==

restart;with(plots,listplot):with(plots,display):runge4 := proc(f1, f2, a, b, h, alpha1, alpha2) local i, n, au1, au2, k11, k12, k21, k22, k31, k32, k41, k42, tmp1, tmp2; n := (b-a)/h; au1 := [alpha1]; au2 := [alpha2]; for i from 0 to n-1 do k11 := evalf( h*f1(a+i*h, op(-1,au1), op(-1,au2))); k12 := evalf( h*f2(a+i*h, op(-1,au1), op(-1,au2))); k21 := evalf( h*f1( a+(i+1/2)*h,op(-1,au1)+k11/2, op(-1,au2)+k12/2)); k22 := evalf( h*f2( a+(i+1/2)*h,op(-1,au1)+k11/2, op(-1,au2)+k12/2)); k31 := evalf( h*f1( a+(i+1/2)*h,op(-1,au1)+k21/2, op(-1,au2)+k22/2)); k32 := evalf( h*f2( a+(i+1/2)*h,op(-1,au1)+k21/2, op(-1,au2)+k22/2)); k41 := evalf( h*f1( a+(i+1)*h,op(-1,au1)+k31, op(-1,au2)+k32)); k42 := evalf( h*f2( a+(i+1)*h,op(-1,au1)+k31, op(-1,au2)+k32)); tmp1:=op(-1,au1)+(1/6)*(k11+2*k21+2*k31+k41); tmp2:=op(-1,au2)+(1/6)*(k12+2*k22+2*k32+k42); au1:=[op(au1),tmp1]; au2:=[op(au2),tmp2]; end do; return [au1,au2]; end proc:################################################################ # y' = u2; # y = u1; # # Gleichung umformen nach u3 und ersetzten ################################################################f1 := (t,u1,u2) -> u2; f2 := (t,u1,u2) -> -sin(u1)-0.2*u2;

NiM+SSNmMUc2ImYqNiVJInRHRiVJI3UxR0YlSSN1MkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlOSZGJUYlRiU=

NiM+SSNmMkc2ImYqNiVJInRHRiVJI3UxR0YlSSN1MkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYtSSRzaW5HRiU2IzklISIiKiYkIiIjRjMiIiI5JkY3RjNGJUYlRiU=

a:=0;

NiM+SSJhRzYiIiIh

b:=50;

NiM+SSJiRzYiIiNd

h:=(b-a)/500;

NiM+SSJoRzYiIyIiIiIjNQ==

n:=(b-a)/h;

NiM+SSJuRzYiIiQrJg==

au := runge4(f1, f2,a,b,h,2,0);

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i:=(33.7-a)/h+1;

NiM+SSJpRzYiJCIlIVEkISIi

op(338,au[1]);

NiMkIis+ZCIzYCUhIzY=

op(338,au[2]);

NiMkIStcc1RNWiEjNg==

plist := []: for i from 1 to n do tmp := [op(i,au[1]), op(i,au[2])]; plist := [op(plist), tmp]; end do:listplot(plist);

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restart;with(plots,listplot):with(plots,display):runge4 := proc(f1, f2, f3, a, b, h, alpha1, alpha2, alpha3) local i, n, au1, au2, au3, k11, k12, k13, k21, k22, k23, k31, k32, k33, k41, k42, k43, tmp1, tmp2, tmp3; n := (b-a)/h; au1 := [alpha1]; au2 := [alpha2]; au3 := [alpha3]; for i from 0 to n-1 do print(i); k11 := evalf( h*f1(a+i*h, op(-1,au1), op(-1,au2), op(-1,au3))); k12 := evalf( h*f2(a+i*h, op(-1,au1), op(-1,au2), op(-1,au3))); k13 := evalf( h*f3(a+i*h, op(-1,au1), op(-1,au2), op(-1,au3))); k21 := evalf( h*f1( a+(i+1/2)*h,op(-1,au1)+k11/2, op(-1,au2)+k12/2, op(-1,au3)+k13/2)); k22 := evalf( h*f2( a+(i+1/2)*h,op(-1,au1)+k11/2, op(-1,au2)+k12/2, op(-1,au3)+k13/2)); k23 := evalf( h*f3( a+(i+1/2)*h,op(-1,au1)+k11/2, op(-1,au2)+k12/2, op(-1,au3)+k13/2)); k31 := evalf( h*f1( a+(i+1/2)*h,op(-1,au1)+k21/2, op(-1,au2)+k22/2, op(-1,au3)+k23/2)); k32 := evalf( h*f2( a+(i+1/2)*h,op(-1,au1)+k21/2, op(-1,au2)+k22/2, op(-1,au3)+k23/2)); k33 := evalf( h*f3( a+(i+1/2)*h,op(-1,au1)+k21/2, op(-1,au2)+k22/2, op(-1,au3)+k23/2)); k41 := evalf( h*f1( a+(i+1)*h,op(-1,au1)+k31, op(-1,au2)+k32,op(-1,au3)+k33)); k42 := evalf( h*f2( a+(i+1)*h,op(-1,au1)+k31, op(-1,au2)+k32, op(-1,au3)+k33)); k43 := evalf( h*f3( a+(i+1)*h,op(-1,au1)+k31, op(-1,au2)+k32, op(-1,au3)+k33)); tmp1:=op(-1,au1)+(1/6)*(k11+2*k21+2*k31+k41); tmp2:=op(-1,au2)+(1/6)*(k12+2*k22+2*k32+k42); tmp3:=op(-1,au3)+(1/6)*(k13+2*k23+2*k33+k43); au1:=[op(au1),tmp1]; au2:=[op(au2),tmp2]; au3:=[op(au3),tmp3]; end do; return [au1,au2,au3]; end proc:c1 := 0.2: c2 := 0.2: c3 := 5.7: f1 := (t,x,y,z) -> -y-z; f2 := (t,x,y,z) -> x+x1*y; f2 := (t,x,y,z) -> c2+y*(x-c3);

NiM+SSNmMUc2ImYqNiZJInRHRiVJInhHRiVJInlHRiVJInpHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwmOSYhIiI5J0YxRiVGJUYlNiM+SSNmMkc2ImYqNiZJInRHRiVJInhHRiVJInlHRiVJInpHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwmOSUiIiIqJkkjeDFHRiVGMTkmRjFGMUYlRiVGJQ==NiM+SSNmMkc2ImYqNiZJInRHRiVJInhHRiVJInlHRiVJInpHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwmSSNjMkdGJSIiIiomOSZGMSwmOSVGMUkjYzNHRiUhIiJGMUYxRiVGJUYl

a:=0;

NiM+SSJhRzYiIiIh

b:=100;

NiM+SSJiRzYiIiQrIg==

n:=10;

NiM+SSJuRzYiIiM1

h:=(b-a)/n;

NiM+SSJoRzYiIiM1

n:=(b-a)/h;

NiM+SSJuRzYiIiM1

au := runge4(f1, f2, f3 ,a,b,h,0,0,0);

NiMiIiE=NiMiIiI=NiMiIiM=NiMiIiQ=NiMiIiU=

NiMiIiY=

Warning, computation interrupted

au1 := [0]: au2 := [0]: au3 := [0]:for i from 0 to n-1 do print(i); k11 := evalf( h*f1(a+i*h, Last(au1), Last(au2), Last(au3))); k12 := evalf( h*f2(a+i*h, Last(au1), Last(au2), Last(au3))); k13 := evalf( h*f3(a+i*h, Last(au1), Last(au2), Last(au3))); k21 := evalf( h*f1( a+(i+1/2)*h, Last(au1)+k11/2, Last(au2)+k12/2, Last(au3)+k13/2)); k22 := evalf( h*f2( a+(i+1/2)*h, Last(au1)+k11/2, Last(au2)+k12/2, Last(au3)+k13/2)); k23 := evalf( h*f3( a+(i+1/2)*h, Last(au1)+k11/2, Last(au2)+k12/2, Last(au3)+k13/2)); k31 := evalf( h*f1( a+(i+1/2)*h, Last(au1)+k21/2, Last(au2)+k22/2, Last(au3)+k23/2)); k32 := evalf( h*f2( a+(i+1/2)*h, Last(au1)+k21/2, Last(au2)+k22/2, Last(au3)+k23/2)); k33 := evalf( h*f3( a+(i+1/2)*h, Last(au1)+k21/2, Last(au2)+k22/2, Last(au3)+k23/2)); k41 := evalf( h*f1( a+(i+1)*h, Last(au1)+k31, Last(au2)+k32, Last(au3)+k33)); k42 := evalf( h*f2( a+(i+1)*h, Last(au1)+k31, Last(au2)+k32, Last(au3)+k33)); k43 := evalf( h*f3( a+(i+1)*h, Last(au1)+k31, Last(au2)+k32, Last(au3)+k33)); au1 := Append(au1, Last(au1)+(1/6)*(k11+2*k21+2*k31+k41)); au2 := Append(au2, Last(au2)+(1/6)*(k12+2*k22+2*k32+k42)); au3 := Append(au3, Last(au3)+(1/6)*(k13+2*k23+2*k33+k43)); end do: au1; au2; au3;

i:=(88.9-a)/h+1;

NiM+SSJpRzYiJCIlKyopISIi

op(890,au[1]);op(890,au[2]);op(890,au[3]);

plist := []: for i from 1 to n do tmp := [op(i,au[1]), op(i,au[2])]; plist := [op(plist), tmp]; end do:listplot(plist);

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solve( {x*(c1*y-c2) = 0, y*(c3-c4*x) = 0}, {x,y} );

NiQ8JC9JInhHNiIkIiIhRigvSSJ5R0YmRic8JC9GKiQiJCsmRigvRiUkIiUrOkYo

solve( {-y-z=0, x+c1*y=0, c2+z*(x-c3)=0}, {x,y,z});

NiQ8JS9JInlHNiIkISs8QzU4TiEjNi9JInhHRiYkIitNWz9FcSEjNy9JInpHRiYkIis8QzU4TkYpPCUvRiUkISspKm9bWUchIikvRjAkIispKm9bWUdGNy9GKyQiKyZ6dEhwJiEiKg==

au := runge4(f1, f2,a,b,h,1500, 500);

NiM+SSNhdUc2IjckN2VpbiIlKzokRigiIiFGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRik3ZWluIiQrJiRGLEYqRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYtRi1GLUYt

plist := []: for i from 1 to n do tmp := [op(i,au[1]), op(i,au[2])]; plist := [op(plist), tmp]; end do:listplot(plist);

LSUlUExPVEc2JC0lJ0NVUlZFU0c2IzdkaW43JCQiJSs6IiIhJCIkKyZGLEYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKUYpRilGKS0lJUZPTlRHNiQlKkhFTFZFVElDQUciIzU=

restart;with(plots,listplot):with(plots,display):runge4 := proc(f1, f2, a, b, h, alpha1, alpha2) local i, n, au1, au2, k11, k12, k21, k22, k31, k32, k41, k42, tmp1, tmp2; n := (b-a)/h; au1 := [alpha1]; au2 := [alpha2]; for i from 0 to n-1 do k11 := evalf( h*f1(a+i*h, op(-1,au1), op(-1,au2))); k12 := evalf( h*f2(a+i*h, op(-1,au1), op(-1,au2))); k21 := evalf( h*f1( a+(i+1/2)*h,op(-1,au1)+k11/2, op(-1,au2)+k12/2)); k22 := evalf( h*f2( a+(i+1/2)*h,op(-1,au1)+k11/2, op(-1,au2)+k12/2)); k31 := evalf( h*f1( a+(i+1/2)*h,op(-1,au1)+k21/2, op(-1,au2)+k22/2)); k32 := evalf( h*f2( a+(i+1/2)*h,op(-1,au1)+k21/2, op(-1,au2)+k22/2)); k41 := evalf( h*f1( a+(i+1)*h,op(-1,au1)+k31, op(-1,au2)+k32)); k42 := evalf( h*f2( a+(i+1)*h,op(-1,au1)+k31, op(-1,au2)+k32)); tmp1:=op(-1,au1)+(1/6)*(k11+2*k21+2*k31+k41); tmp2:=op(-1,au2)+(1/6)*(k12+2*k22+2*k32+k42); au1:=[op(au1),tmp1]; au2:=[op(au2),tmp2]; end do; return [au1,au2]; end proc:eul_mod := proc(f1, f2, a, b, h, alpha1, alpha2) local i, n, au1, au2, k11, k12, k21, k22, k31, k32, k41, k42, tmp1, tmp2; n := (b-a)/h; au1 := [alpha1]; au2 := [alpha2]; for i from 0 to n-1 do #tmp1 := op(-1,au1)+h/2*(f1(t(i),op(-1,au1),op(-1,au2))+f1(t(i+1),op(-1,au1)+h*f1(t(i),op(-1,au1),op(-1,au2)),op(-1,au2)+h*f1(t(i),op(-1,au1),op(-1,au2)))); #tmp2 := op(-1,au1)+h/2*(f2(t(i),op(-1,au1),op(-1,au2))+f2(t(i+1),op(-1,au1)+h*f2(t(i),op(-1,au1),op(-1,au2)),op(-1,au2)+h*f2(t(i),op(-1,au1),op(-1,au2)))); tmp1 := op(-1,au1)+(h/2)*(f1(t(i),op(-1,au1),op(-1,au2))+f1(t(i+1),op(-1,au1)+h*f1(t(i),op(-1,au1),op(-1,au2)),op(-1,au1)+h*f1(t(i),op(-1,au1),op(-1,au2)))); tmp2 := op(-1,au1)+(h/2)*(f2(t(i),op(-1,au1),op(-1,au2))+f1(t(i+1),op(-1,au1)+h*f2(t(i),op(-1,au1),op(-1,au2)),op(-1,au1)+h*f2(t(i),op(-1,au1),op(-1,au2)))); au1:=[op(au1),evalf(tmp1)]; au2:=[op(au2),evalf(tmp2)]; end do; return [au1,au2]; end proc:################################################################ # y' = u2; # y = u1; # # Gleichung umformen nach u3 und ersetzten ################################################################f1 := (t,u1,u2) -> u2; f2 := (t,u1,u2) -> -sin(u1)-0.2*u2;

NiM+SSNmMUc2ImYqNiVJInRHRiVJI3UxR0YlSSN1MkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlOSZGJUYlRiU=

NiM+SSNmMkc2ImYqNiVJInRHRiVJI3UxR0YlSSN1MkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYtSSRzaW5HNiRJKnByb3RlY3RlZEdGMkkoX3N5c2xpYkdGJTYjOSUhIiIqJiQiIiNGNiIiIjkmRjpGNkYlRiVGJQ==

a:=0;

NiM+SSJhRzYiIiIh

b:=50;

NiM+SSJiRzYiIiNd

n:=50;

NiM+SSJuRzYiIiNd

h:=(b-a)/n;

NiM+SSJoRzYiIiIi

n:=(b-a)/h;

NiM+SSJuRzYiIiNd

au := eul_mod(f1, f2,a,b,h,2,0);

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

i:=(33.7-a)/h+1;

NiM+SSJpRzYiJCIkWiQhIiI=

op(34,au[1]);

NiMkIit1OU1PNiIiIw==

op(338,au[1]);

Error, improper op or subscript selector

op(338,au[2]);

NiMkIStcc1RNWiEjNg==