Question

求助！Matlab四阶R-K法求解一个二阶非线性微分方程；x’’+x^3/(1+x^2)=0;初始条件 x（0）=A x’（0）=0

希望能够给出matlab的程序，和x（t)的图像

Answer 1

clc

A=1;

h=0.01;

x=[A 0]

X=[];

t=0:h:20;

for i=1:length(t)

    X_1 = Runge_Kutta_4(t(i),x,@matlab4rk,h);

    X=[X;t(i),X_1];

    x=X_1;

end

string1=['A=',num2str(A)];

A=2;

h=0.01;

x=[A 0]

X1=[];

t=0:h:20;

for i=1:length(t)

    X1_1 = Runge_Kutta_4(t(i),x,@matlab4rk,h);

    X1=[X1;t(i),X1_1];

    x=X1_1;

end

plot(X(:,1),X(:,2),'-k',X1(:,1),X1(:,2),'-b','linewidth',2);

hold on

grid on

xlabel('t-time','fontsize',14)

ylabel('x','fontsize',14)

tstring=['x"+x^3/(1+x^2)=0'];

title(tstring,'fontsize',14);

string2=['A=',num2str(A)];

legend(string1,string2)

    

function Y = Runge_Kutta_4(t,X,f,h)

    K1=f(t,X);

    K2=f(t+h/2,X+h/2*K1);

    K3=f(t+h/2,X+h/2*K2);

    K4=f(t+h,X+h*K3);

    Y=X+h/6*(K1+2*K2+2*K3+K4);

function dx=matlab4rk(t,x)

% x1=x;x2=x'

dx=zeros(1,2);

dx(1)=x(2);

dx(2)=-x(1)^3/(1+x(1)^2);

追问

真的很感谢你，这个问题已经苦恼我很久了，thank you very much！！