基于Matlab实现求解常微分方程数值（源码）.rar

clear;clc; y0 = [0 1]; h = 0.1; tspan = [0 10]; N = 1/h +1 ; alphat = [0.01 0.99]; ah = 0.01; MM = (alphat(2) -alphat(1))/ah ; T = []; global a for a=alphat(1):ah:alphat(2) varphi = sqrt(3)/pi*log(a/(1-a)); [y,~] = RepMilneHammin(@example2,tspan,y0,h); [yy,~] = MilneHammin(@example2,tspan,y0,h); [yyy,~] = RungeKutta4(@example2,tspan,y0,h); [yyyy,t] = AdamsSimpson(@example2,tspan,y0,h); M = length(t); z = (exp(t+varphi*t)-1)/(1+varphi); T = [T;y(N,1),yy(N,1),yyy(N,1),yyyy(N,1),z(N,1)]; % e = sum((y(:,1)-z).^2)/M; % ee = sum((yy(:,1)-z).^2)/M; % eee = sum((yyy(:,1)-z).^2)/M; % eeee = sum((yyyy(:,1)-z).^2)/M; % [e,ee,eee,eeee] % % figure % plot(t,y(:,1),t,yy(:,1),t,yyy(:,1),t,yyyy(:,1),t,z); end alpha = alphat(1):ah:alphat(2); alpha = alpha'; plot(T(:,1),alpha,'-o',T(:,2),alpha,'-.',T(:,3),alpha,'-*',T(:,4),alpha,'-x',T(:,5),alpha); legend('RepMilneHammin','MilneHammin','RungeKutta4','AdamsSimpson','Exact solution') xlabel('x_{t}^{\alpha}','FontName','times new Roman','FontSize',15) ylabel('\alpha','FontName','times new Roman','FontSize',15); MSE = [sum((T(:,1)-T(:,5)).^2)/MM,sum((T(:,2)-T(:,5)).^2)/MM,sum((T(:,3)-T(:,5)).^2)/MM,sum((T(:,4)-T(:,5)).^2)/MM]; MAE = [sum(abs(T(:,1)-T(:,5)))/MM,sum(abs(T(:,2)-T(:,5)))/MM,sum(abs(T(:,3)-T(:,5)))/MM,sum(abs(T(:,4)-T(:,5)))/MM]; MSE MAE