A new quintic B-spline approximation for numerical treatment of Boussinesq equation

Volume 20, Issue 1, pp 30--42 http://dx.doi.org/10.22436/jmcs.020.01.04
Publication Date: August 28, 2019 Submission Date: April 19, 2019 Revision Date: May 30, 2019 Accteptance Date: July 01, 2019

Authors

Tahir Nazir - Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan. Muhammad Abbas - Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan. Muhammad Kashif Iqbal - Department of Mathematics, Government College University, 38000 Faisalabad, Pakistan.


Abstract

In this work, we have presented a new quintic B-spline approximation technique for numerical solution of Boussinesq equation. Usual finite difference formulation has been applied to discretize the problem in temporal domain, whereas, the typical fifth degree B-spline functions, equipped with a new approximation for fourth order derivative, have been utilized to interpolate the unknown function in spatial direction. The stability and error analysis of the proposed numerical algorithm have been studied rigorously. Two test examples are considered to affirm the performance and accuracy of the new scheme. The computational outcomes are found to be better than the existing numerical techniques on the topic.


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