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Mathematical Models and Computer Simulations

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01-11-2019

Simulation of Generalized Nonlinear Fourth Order Partial Differential Equation with Quintic Trigonometric Differential Quadrature Method

Authors: Geeta Arora, Varun Joshi

Published in: Mathematical Models and Computer Simulations | Issue 6/2019

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Abstract

This paper aims to focus on the implementation of a new approach, quintic trigonometric B-spline basis functions in differential quadrature method to find numerical solution of generalized fourth order partial differential equations with nonlinearity involved. The obtained results using this approach are presented in comparison with available exact and numerical solutions obtained by other researchers. The obtained solutions are in agreement with the available exact solutions and even better than the solutions proposed by the other schemes in the literature. The applicability of the scheme are demonstrated by different eight test problems for the discussed equations that are simulated, for calculating errors like L₂, \({{L}_{\infty }}\), RMS and GRE. To visualize the same, solutions are also presented graphically along with the exact solutions. Scheme is shown to be unconditionally stable with the help of eigenvalues, which demonstrates the consistency of the proposed numerical scheme.

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Title: Simulation of Generalized Nonlinear Fourth Order Partial Differential Equation with Quintic Trigonometric Differential Quadrature Method
Authors: Geeta Arora
Varun Joshi
Publication date: 01-11-2019
Publisher: Pleiades Publishing
Published in: Mathematical Models and Computer Simulations / Issue 6/2019
Print ISSN: 2070-0482
Electronic ISSN: 2070-0490
DOI: https://doi.org/10.1134/S207004821906005X

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