Solving Second Order Non-Linear Boundary Value Problems by Four Numerical Methods


The boundary value problems for the 2nd order non-linear ordinarydifferential equations are solved by using four numerical methods. Thesenumerical methods are Rung-Kutta of 4th order, Rung–Kutta Butcher of 6th order,differential transformation method, and the Homotopy perturbation method. Threephysical problems from the literature are solved by the four methods for comparingthe results. The results were presented in tables and figures. The differentialtransformation method appeared to be effective and reliable to find the seminumerical-analytical solutions for such type of boundary value problems.