Runge-Kutta 4th order method for two variable

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Mohammad Sh 2021-7-22

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/883639-runge-kutta-4th-order-method-for-two-variable

评论： James Tursa 2021-7-22

clc
clear
syms x1 x2
a=3;
b=5;
c=7;
d=2;
t(1)=0;
X1(1)=1;
X2(1)=-1;
TG=5;
n=100;
h=(TG-t(1))/n;
fx1=inline(x2);
fx2=inline(-a*x1+b*x1^2);
for i=1:n
    K1_1=h*fx1(X2(i));
    K2_1=h*fx1(X2(i)+K1_1/2);
    K3_1=h*fx1(X2(i)+K2_1/2);
    K4_1=h*fx1(X2(i)+K3_1);
    X1(i+1)=X1(i)+(1/6)*(K1_1+2*K2_1+2*K3_1+K4_1);
    K1=h*fx2(X1(i));
    K2=h*fx2(X1(i)+K1_1/2);
    K3=h*fx2(X1(i)+K2_1/2);
    K4=h*fx2(X1(i)+K3_1);
    X2(i+1)=X2(i)+(1/6)*(K1+2*K2+2*K3+K4);
    t(i+1)=t(i)+h;
    disp('  ')
    disp(['t(',num2str(i),'): ',num2str(t(i+1))])
    disp(['X1(',num2str(i),'): ',num2str(X1(i+1))])
    disp(['X2(',num2str(i),'): ',num2str(X2(i+1))])
end
disp('  ')
subplot(1,3,1)
plot(t,'r--*')
title('t')
subplot(1,3,2)
plot(X1,'-.o')
title('X1')
subplot(1,3,3)
plot(X2,'-.*')
title('X2')