LAPLACE-SPECTRAL COLLOCATION-TAU METHOD FOR SOLVING BOUNDARY VALUE PROBLEMS |Asian Journal of Math

The numerical solution of pth order boundary value problems is presented in this study using a direct solution technique. The concept behind this method is to break the perturbation term into two parts, namely (p1/p)Hp(x) and 1/pHp(x). The former is then added to the pth derivative's truncated series of Chebyshev expansion, after which successive integrations are performed to obtain approximate expressions for the function's lower-order derivatives and the function itself, while the latter is added to the right-hand side of the given differential equation. The Laplace transform of the slightly altered equation is then used to create a new trial function. Four cases are considered for numerical illustration of the procedure, and the findings produced are compared to some well-known results in the literature. The results show that the current method for solving boundary value problems is accurate and trustworthy.

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