Euler Method without using ODE solvers such as ode45
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I am trying to write a code that will solve a first order differential equation using Euler's method. I do not want to use an ode solver but rather would like to use numerical methods which allow me to calculate slope (k1, k2 values, etc). I am given an equation with two different step values. I am not sure how to begin to write this in MATLAB. I have solved the equation by hand and am now trying to write a code that solves that equation.
The equation to be used is y’ +2y = 2 – e -4t.
y(0) = 1, which has an exact solution:
y(t) = 1 + 0.5 e -4t - 0.5 e -2t .
I did the following to solve numerically: 1+(0.5e^-4t) - (0.5e^-2(0)) y_n+1=1+0.1 and y_n+1=1+1(.001)
The step sizes are 0.1 and 0.001. (so my h in this example). The t values range from 0.1 to 5.0.
Any help is appreciated even if its an example pseudocode. Thank you