A new algorithm based on spline in tension approximation for 1D quasi-linear parabolic equations on a variable mesh

作者：Talwar Jyoti; Mohanty R K^*; Singh Swarn

来源：International Journal of Computer Mathematics, 2016, 93(10): 1771-1786.

DOI：10.1080/00207160.2015.1074682

• quasi-linear parabolic equations
• spline in tension
• non-polynomial spline
• stability analysis
• variable mesh
• Burgers' equation

In this paper, we propose a new two-level implicit method of order two in time and four in space directions, based on spline in tension approximation for the numerical solution of one space dimensional quasi-linear parabolic partial differential equation on a uniform mesh. We have discussed the derivation of the proposed method in detail and have also discussed the stability analysis for a model problem. We have extended the method to non-uniform mesh. Numerical results are given to illustrate the usefulness of the proposed methods.

• 出版日期2016