A new high accuracy off-step cubic spline approximations on a quasi-variable mesh for the system of nonlinear parabolic equations in one space dimension. Issue 2 (29th November 2020)

• Record Type: Journal Article
• Authors: Mohanty, R. K.; Mittal, Kajal; Kaur, Deepti
• Is Part Of: International journal for computational methods in engineering science and mechanics. Volume 22:Issue 2(2021)
• Page Start: 123
• Page End: 137
• Publication Date: 2020-11-29
• Subjects: Cubic spline approximations -- quasi-variable mesh -- nonlinear parabolic equations -- Fisher-Kolmogorov equation -- Kuramoto-Sivashinsky equation -- coupled Burgers' and Burgers-Huxley equations; 65M06 -- 65M12 -- 65M22 -- 65Y20; Engineering -- Data processing -- Periodicals; Engineering mathematics -- Periodicals; Computer-aided engineering -- Periodicals; 620.00420285
• DOI: 10.1080/15502287.2020.1853852
• Languages: English
• ISSNs: 1550-2287

Abstract

Abstract: We study a new two-level implicit method of order two in time and three in space based on two off-step points and an in-between point for the system of 1D nonlinear parabolic equations on a quasi-variable mesh. The proposed method is derived directly from the consistency condition of cubic spline polynomial approximation. The method is unconditionally stable, when tested on a model equation. We solve the Fisher-Kolmogorov equation, the Kuramoto-Sivashinsky equation, coupled Burgers' and the Burgers-Huxley equations to demonstrate the usefulness of the proposed method. The numerical results confirm the stability character of the method for large Reynolds number.