Decatic B‐spline collocation scheme for approximate solution of Burgers' equation

Abstract

A decatic B‐spline collocation technique is employed to compute the numerical result of a nonlinear Burgers' equation. The nonlinear term of Burgers' equation is locally linearized using Taylor series technique. The present method is effective for the approximate solution of Burgers' with a very small value of kinematic viscosity “a.” Some illustrated numerical experiments are taken into consideration to focus on the importance of the current work and some comparative studies are reported with others as well as with the exact solutions. The linear stability of the method is analyzed with Von Neumann technique. Application of higher‐order derivatives rather than lower‐order derivatives of the decatic B‐splines on the boundary conditions is the keynote to obtain a better approximate solution of the present method.

A novel approach for numerical treatment of traveling wave solution of ion acoustic waves as a fractional nonlinear evolution equation on Shehu transform environment

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A reliable method for voltage of telegraph equation in one and two space variables in electrical transmission: approximate and analytical approach

“…Dhegihan, Ghesmati [2] implemented both boundary integral equation and dual reciprocity method for obtaining the approximate solution of two space telegraph equation. B-spline collocation for nonlinear partial differential equations by Jena and Gebremedhin [31][32][33][34], numerical solitons in B-spline environment by Jena et al [35,36] and Generalized Rosenau-RLW equation in B-spline scheme via BFRK approach by Senapati and Jena [37,38] have played a vital role towards this manuscript. The SDIQR mathematical modelling for Covid-19 of Odisha based on Laplace Adomian decomposition method is employed by Sahu and Jena [30] and Jena and Sahu [58] solved the fractional nonlinear evolution equation by using Shehu transform.…”

Numerical treatment of Kuramoto-Sivashinsky equation on B-spline collocation

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