2阶泰勒方法求解常微分方程测试程序

% 2阶泰勒方法求解常微分方程测试程序 clear clc close all Hfun = @Dfun; % 参数 t = [0 12]; % 时间范围 x0 = [0 1 1]; % 初始状态 %% 步长h = 0.1 h = 0.1; % 时间步长 % 改进欧拉法求解 [T0,X0] = ODE_Taylor2( Hfun,t,h,x0 ); % 向前欧拉法求解 [T1,X1] = ODE_ExplicitEuler( Hfun,t,h,x0 ); % 改进欧拉法求解 [T2,X2] = ODE_ImprovedEuler( Hfun,t,h,x0 ); % Matlab自带ode45求解 [T3,X3] = ode45( Hfun,t(1):h:t(2),x0 ); % 绘图对比 figure subplot(311) plot(T0,X0(:,1),T1,X1(:,1),T2,X2(:,1),T3,X3(:,1)) xlabel('Time(s)') ylabel('x_1') legend('二阶泰勒法','向前欧拉法','改进欧拉法','ode45') subplot(312) plot(T0,X0(:,2),T1,X1(:,2),T2,X2(:,2),T3,X3(:,2)) xlabel('Time(s)') ylabel('x_2') legend('二阶泰勒法','向前欧拉法','改进欧拉法','ode45') subplot(313) plot(T0,X0(:,3),T1,X1(:,3),T2,X2(:,3),T3,X3(:,3)) xlabel('Time(s)') ylabel('x_3') legend('二阶泰勒法','向前欧拉法','改进欧拉法','ode45') %% 步长h = 0.6 h = 0.6; % 时间步长 % 改进欧拉法求解 [T0,X0] = ODE_Taylor2( Hfun,t,h,x0 ); % 改进欧拉法求解 [T2,X2] = ODE_ImprovedEuler( Hfun,t,h,x0 ); % Matlab自带ode45求解 [T3,X3] = ode45( Hfun,t(1):h:t(2),x0 ); % 绘图对比 figure subplot(311) plot(T0,X0(:,1),T2,X2(:,1),T3,X3(:,1)) xlabel('Time(s)') ylabel('x_1') legend('二阶泰勒法','改进欧拉法','ode45') subplot(312) plot(T0,X0(:,2),T2,X2(:,2),T3,X3(:,2)) xlabel('Time(s)') ylabel('x_2') legend('二阶泰勒法','改进欧拉法','ode45') subplot(313) plot(T0,X0(:,3),T2,X2(:,3),T3,X3(:,3)) xlabel('Time(s)') ylabel('x_3') legend('二阶泰勒法','改进欧拉法','ode45') %% 步长h = 0.9 h = 0.9; % 时间步长 % 改进欧拉法求解 [T0,X0] = ODE_Taylor2( Hfun,t,h,x0 ); % 改进欧拉法求解 [T2,X2] = ODE_ImprovedEuler( Hfun,t,h,x0 ); % Matlab自带ode45求解 [T3,X3] = ode45( Hfun,t(1):h:t(2),x0 ); % 绘图对比 figure subplot(311) plot(T0,X0(:,1),T2,X2(:,1),T3,X3(:,1)) xlabel('Time(s)') ylabel('x_1') legend('二阶泰勒法','改进欧拉法','ode45') subplot(312) plot(T0,X0(:,2),T2,X2(:,2),T3,X3(:,2)) xlabel('Time(s)') ylabel('x_2') legend('二阶泰勒法','改进欧拉法','ode45') subplot(313) plot(T0,X0(:,3),T2,X2(:,3),T3,X3(:,3)) xlabel('Time(s)') ylabel('x_3') legend('二阶泰勒法','改进欧拉法','ode45')