Cardinal-type approximations for conservation laws of mixed type

Kamel Al-Khaled

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Nonlinear partial differential equations appear in many branches of physics, engineering and applied mathematics. This paper provides a technical description of the application of collocation interpolation methods based on Sinc functions to conservation laws of mixed hyperbolic-elliptic type, with Riemann type conditions. Sinc approximations to both derivatives and indefinite integrals reduces the solution to an explicit system of algebraic equations. The nonlinear terms are easily handled with the help of Hadamard matrix multiplications. The error in the solution is shown to converge to the exact solution at an exponential rate. The convergence proof of the solution for the discrete system is given using fixed-point iteration. The scheme is numerically tested on the Van der Waals equation in fluid dynamics. Easy and economical implementation is the strength of this method.

Original languageEnglish
Pages (from-to)423-433
Number of pages11
JournalNonlinear Studies
Volume21
Issue number3
Publication statusPublished - 2014

Fingerprint

Sinc Function
Indefinite integral
Fixed Point Iteration
Hadamard Matrix
Matrix multiplication
Van Der Waals
Interpolation Method
Fluid Dynamics
Collocation Method
Applied mathematics
Discrete Systems
Nonlinear Partial Differential Equations
Algebraic Equation
Conservation Laws
Conservation
Branch
Exact Solution
Physics
Engineering
Converge

Keywords

  • Conservation laws of mixed type
  • Numerical solutions
  • Sinc-collocation
  • Van der waals equation

ASJC Scopus subject areas

  • Applied Mathematics
  • Modelling and Simulation

Cite this

Cardinal-type approximations for conservation laws of mixed type. / Al-Khaled, Kamel.

In: Nonlinear Studies, Vol. 21, No. 3, 2014, p. 423-433.

Research output: Contribution to journalArticle

Al-Khaled, Kamel. / Cardinal-type approximations for conservation laws of mixed type. In: Nonlinear Studies. 2014 ; Vol. 21, No. 3. pp. 423-433.
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