An improvised technique of quintic Hermite splines to discretize generalized Burger Huxley type equations

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 16 اردیبهشت 1401  

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.75871.1120

نویسندگان

Inderpreet Kaur¹؛ Shelly Arora ²؛ Indu Bala²

¹Chitkara University Institute of Engineering and Technology, Department of Applied Sciences, Chitkara University, Patiala, Punjab, INDIA

²Department of Mathematics, Punjabi University, Patiala, Punjab-147002, INDIA

چکیده

A mathematical collocation solution for generalized Burgers-Huxley and generalized Burger Fisher equation has been monitored using the weighted residual method with Hermite splines. In the space direction, quintic Hermite splines are introduced, while the time direction is discretized using a finite difference approach. The technique is determined to be unconditionally stable, with order ($h^{4}+\triangle t$) convergence. The technique's efficacy is tested using nonlinear partial differential equations. Two problems of the generalized Burger Huxley and Burger Fisher equation have been solved using a finite difference scheme as well as the quintic Hermite collocation method (FDQHCM) with varying impacts. The FDQHCM computer codes are written in MATLAB without transforming the nonlinear term to a linear term. The numerical findings are reported in weighted norms and in discrete form. To assess the technique's applicability, numerical and exact values are compared, and a reasonably good agreement is recognized between the two.

کلیدواژه‌ها

Quintic Hermite splines؛ Forward finite difference scheme؛ collocation method؛ stability analysis