LAPLACE-SPECTRAL COLLOCATION-TAU METHOD FOR SOLVING BOUNDARY VALUE PROBLEMS

This paper presents a direct solution technique for the numerical solution of pth order boundary value problems. The whole idea of this method is based on the splitting of perturbation term into two, namely,(p−1/p)Hp(x) and 1/pHp(x) . The former is then added to truncated series of Chebyshev expansion which represents the pth derivative, after which successive integrations are carried out to obtain approximate expressions for its lower-order derivatives and the function itself, while the latter is added to the right-hand side of the given differential equation. A new trial function is thereafter obtained by taking the Laplace transform of the slightly perturbed equation. For the numerical illustration of the method, four examples are considered and the results obtained are compared with some well-known results in the literature. From the results, it is observed that the present method is accurate and reliable for solving boundary value problems.