### 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 language | English |
---|---|

Pages (from-to) | 423-433 |

Number of pages | 11 |

Journal | Nonlinear Studies |

Volume | 21 |

Issue number | 3 |

Publication status | Published - 2014 |

### Fingerprint

### 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

*Nonlinear Studies*,

*21*(3), 423-433.

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

Research output: Contribution to journal › Article

*Nonlinear Studies*, vol. 21, no. 3, pp. 423-433.

}

TY - JOUR

T1 - Cardinal-type approximations for conservation laws of mixed type

AU - Al-Khaled, Kamel

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Conservation laws of mixed type

KW - Numerical solutions

KW - Sinc-collocation

KW - Van der waals equation

UR - http://www.scopus.com/inward/record.url?scp=84906846682&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84906846682&partnerID=8YFLogxK

M3 - Article

VL - 21

SP - 423

EP - 433

JO - Nonlinear Studies

JF - Nonlinear Studies

SN - 1359-8678

IS - 3

ER -