2nd order euler method problem

Question

jun seong park 2023-1-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1895565-2nd-order-euler-method-problem

回答： Jan 2023-1-17

在 MATLAB Online 中打开

my brain is boiling

How to solve initial value problem?

x x ̈ +x ̇ ^2+cost=0, x(0)=√6, x ̇ (0)=0

% euler method 2nd order 
clc;
clear;
close all;
h=0.1;
t = 0:h:10; 
n = numel(size(t));
     x = zeros(size(t));
  dxdt = zeros(size(t));
dx2dt2 = zeros(size(t));
   x(1) = sqrt(6);
dxdt(1) = 0;
plot(t,x);
for i = 1:n-1
    dx2dt2(i+1) = dx2dt2(i) + h*f2(t(i),dx2dt2(i));
    dxdt(i+1) = dxdt(i) + h*f1(t(i),dxdt(i));
end
function dx2dt2 = f2(t,x,dxdt)
 dx2dt2 = -(dxdt^2 + cos(t))/x;
end
function dxdt = f1(t,x,dx2dt2)
dxdt = sqrt(cost(t)-x*dx2dt2);
end

also i made another code to slove same problem

% euler method 2nd order 
clc;
clear;
close all;
h=0.1;
t = 0:h:10; 
n = numel(size(t));
     x = zeros(size(t));
  dxdt = zeros(size(t));
dx2dt2 = zeros(size(t));
   x(1) = sqrt(6);
dxdt(1) = 0;
f2 = @(t,x,dxdt) -(dxdt^2 + cos(t))/x;
f1 = @(t,x,dx2dt2) sqrt(cost(t)-x*dx2dt2);
for i = 1:n-1
    dx2dt2(i+1) = dx2dt2(i) + h*f2(t(i),dx2dt2(i));
    dxdt(i+1) = dxdt(i) + h*f1(t(i),dxdt(i));
end
plot(t,x);