Good luck, and may your matrices always be invertible.
You will often be asked why a method fails. Remember that Newton-Raphson requires a good initial guess, and certain ODE solvers become unstable if the "step size" ( ) is too large. numerical methods for engineers coursera answers
However, let’s be honest: the programming assignments can be brutal. You are not just learning math; you are implementing Newton-Raphson, Gauss-Seidel, and Runge-Kutta methods in MATLAB or Python. This is where the search for begins. Good luck, and may your matrices always be invertible