Single-Step Block Method of P-Stable for Solving Third-Order Differential Equations (IVPs): Ninth Order of Accuracy

Duromola M.K.^1,

¹Department of Mathematical Sciences, Federal University of Technology, Akure PMB 704, Nigeria

Cite this paper

Duromola M.K.. Single-Step Block Method of P-Stable for Solving Third-Order Differential Equations (IVPs): Ninth Order of Accuracy. American Journal of Applied Mathematics and Statistics. 2022; 10(1):4-13. doi: 10.12691/AJAMS-10-1-2

Abstract

The solution of Differential Equations is an important topic for deliberation among scientists. However, until today, nothing is known on a single-step block method of p-stable for solving third-order Differential Equations (IVPs) whose accuracy is ninth order. This paper focuses on the derivation, analysis, and implementation of the one-step implicit hybrid block method with seven off-step points for direct solution of general third-order ordinary differential equations' initial value problems (IVPs). For the solution of IVPs, the power series functions were utilized as the basis function. To determine the unknown parameters, an approximate solution from the basis function was interpolated at chosen off-grid points. The third derivative of the estimated solution was collocated at all grid and off-grid points to produce a system of linear equations. Consistency, zero stability, convergence, and absolute stability were all evaluated on the method. The numerical results achieved through implementation are quite close to the theoretical solutions and compare well to other novel methods in the literature.

Keywords

hybrid block method, grid points, off-grid points, 3^rd Order ODE, implicit

Copyright

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