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This article presents a new numerical scheme to approximate the solution of one-dimensional telegraph equations. With the use of Laplace transform technique, a new form of trial function from the original equation is obtained. The unknown coefficients in the trial functions are determined using collocation method. The efficiency of the new scheme is demonstrated with examples and the approximations are in excellent agreement with the analytical solutions. This method produced better approximations than the ones produced with the standard weighted residual methods.

In this article, the Improved Parker-Sochacki Method (IPSM) is applied to solving nonlinear MichaelisMenten enzyme catalyzed reaction model. The global form of the solution for the concentrations of the substrate, enzyme and the enyzme-free product are obtained. Employing the Laplace-Pade resummation as a post processing technique on the computed series solution, the domain of convergence of the solution is greatly extended. The solution is therefore devoid of limited convergence interval that is typical of series solution of nonlinear differential equations. The proposed method showed a significant improvement over the conventional Parker-Sochacki Method (PSM). Furthermore, comparison of the results with numerically computed solutions via Runge-Kutta method elucidated the simplicity and accuracy of the proposed method.

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