龙格库塔求解一阶微分方程组的MATLAB编程 龙格库塔法求解一阶常微分方程组 的Matlab代码
\u9f99\u683c\u5e93\u5854\u6c42\u89e3\u4e8c\u9636\u5fae\u5206\u65b9\u7a0b\u7ec4\u7684MATLAB\u7f16\u7a0bMATLAB\u6c42\u89e3x''+0.7x'+0.8x'|x'|+25.6x-25.6x³=0\u4e8c\u9636\u5fae\u5206\u65b9\u7a0b\u7ec4\u7684\u65b9\u6cd5\uff0c\u53ef\u4ee5\u6309\u4e0b\u5217\u6b65\u9aa4\u8fdb\u884c\uff1a
1\u3001\u5efa\u7acb\u81ea\u5b9a\u4e49\u51fd\u6570func\uff08\uff09
function f = func(t,x)
%x''+0.7x'+0.8x'|x'|+25.6x-25.6x³=0
f(1)=x(2);
f(2)=25.6*x(1)^3-25.6*x(1)-0.8*x(2)*abs(x(2))-0.7*x(2);
f=f(:);
2\u3001\u5efa\u7acb\u9f99\u683c\u5e93\u5854\u7b97\u6cd5\u51fd\u6570runge_kutta\uff08\uff09
\u8c03\u7528\u683c\u5f0f\uff1a[t,x] = runge_kutta(@(t,x)func(t,x),x0,h,a,b);
3\u3001\u7136\u540e\u6839\u636ex\u548cx'\u6570\u636e\uff0c\u7ed8\u5236\u51fax(t)\u3001x\u2032(t)\u7684\u56fe\u5f62\u3002
plot\uff08x\uff08\uff1a\uff0c1\uff09,x\uff08\uff1a\uff0c2\uff09\uff09
clc
f=@(y,t)([1.65e-3*(14.93-y(1))-1.70e13*exp(-9064.23/y(2))*y(1);
4.93-0.01655*y(2)+1.117e13*exp(-9064.23/y(2))*y(1)]);
[Ca T]=ode45(f,[0 1],[.8 300])
用龙格库塔求解二阶微分方程组的实现方法:
ⅹ0=[0.5 0];
h=0.1;
a=0;b=1;
[t,x] = runge_kutta(@(t,x)func(t,x),x0,h,a,b);
disp(' t x(t) x’(t)')
A=[t',x'];
disp(A)
figure,plot(t,x,'.-'),grid on
xlabel('t'),ylabel('x(t),x’(t)');
title('函数图');
legend('x(t)','x’(t)')
figure,plot(x(:,1),x(:,2),'.-','LineWidth',1.5),grid on
xlabel('x(t)'),ylabel('x’(t)');
title('x(t)—x’(t)函数图');
end
function f = func(t,x)
%x''+0.7x'+0.8x'|x'|+25.6x-25.6x³=0
f(1)=x(2);
f(2)=25.6*x(1)^3-25.6*x(1)-0.8*x(2)*abs(x(2))-0.7*x(2);
f=f(:);
end
绛旓細f(2)=25.6*x(1)^3-25.6*x(1)-0.8*x(2)*abs(x(2))-0.7*x(2);f=f(:);end
绛旓細e(n, 2) = -a(0) * z(1) / a(n) + (b(0) - b(n) * a(0) / a(n)) * u z(n) = X(n) + DT * e(n, 2) / 2 '璁＄畻e(1,3),e(2,3),e(3,3)..e(n,3)For i = 1 To n - 1 e(i, 3) = -a(n - i) * z(1) / a(n) + z(i + 1) + ...
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