Matrix Based Operatorial Approach to Differential and Integral Problems
Damian Trif · InTech eBooks · 2011
are also included in this general form. Moreover, nonlinear problems where the r.h.s. f (x) is replaced by f (x, y(x), y′(x), ..., y(m−1)(x)) can be solved using Newton’s method in the functional space Cm [a, b] by solving a sequence of linear problems (1)+(2). MATLAB uses different methods to solve initial condition problems (ode family) or boundary value problems (bvp4c or bvp5c) based on Runge-Kutta, Adams-Bashforth-Moulton, BDF algorithms, etc. One of the most effective methods for solving (1)+(2) is to shift the problem to the interval [−1, 1] and then to use the Chebyshev spectral methods, i.e. to approximate the solution y by a finite sum of the Chebyshev series