A New Two-Level Implicit Scheme for the System of 1D Quasi-Linear Parabolic Partial Differential Equations Using Spline in Compression Approximations

• Published in: Differential equations and dynamical systems Vol. 27; no. 1-3; pp. 327 - 356
• Main Authors: Mohanty, R. K., Sharma, Sachin, Singh, Swarn
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.01.2019; Springer Nature B.V
• Subjects: Boundary conditions; Computer Science; Engineering; Finite element method; Fluid flow; High Reynolds number; Mathematical models; Mathematics; Mathematics and Statistics; Original Research; Partial differential equations; Polynomials; Reynolds number; Spline functions; Stability analysis; Generalized Burgers–Huxley equations; 65M06; Coupled Burgers’ equation; Newton’s iterative method; 65Y20; 65M22; Quasi-linear parabolic equations; Spline in compression; 65M12

In this article, we proposed a new two-level implicit method of accuracy two in time and four in space based on spline in compression approximations using two half-step points and a central point on a uniform mesh for the numerical solution of the system of 1D quasi-linear parabolic partial differen...