Numerical Method for 2D Quasi-linear Hyperbolic Equation on an Irrational Domain: Application to Telegraphic Equation

Authors

  • Bishnu Pada Ghosh Department of Mathematics, Jagannath University, Dhaka 1100, Bangladesh
  • Nepal Chandra Roy Department of Mathematics, Dhaka University, Dhaka 1000, Bangladesh

DOI:

https://doi.org/10.3329/dujs.v69i2.56492

Keywords:

Quasi-linear; Unequal mesh; Irrational domain; Telegraphic equation; Van der Pol equation; Dissipative equation

Abstract

We develop a novel three-level compact method (implicit) of second order in time and space directions using unequal grid for the numerical solution of 2D quasi-linear hyperbolic partial differential equations on an irrational domain. The stability analysis of the model problem for unequal mesh is discussed and it is revealed that the developed scheme is unconditionally stable for the Telegraphic equation. For linear difference equations on an irrational domain, the alternating direction implicit method is discussed. The projected technique is scrutinized on several physical problems on an irrational domain to exhibitthe accuracy and effectiveness of the suggested method.

Dhaka Univ. J. Sci. 69(2): 116-123, 2021 (July)

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Published

2021-12-01

How to Cite

Ghosh, B. P. ., & Roy, N. C. (2021). Numerical Method for 2D Quasi-linear Hyperbolic Equation on an Irrational Domain: Application to Telegraphic Equation. Dhaka University Journal of Science, 69(2), 116–123. https://doi.org/10.3329/dujs.v69i2.56492

Issue

Vol. 69 No. 2 (2021)

Section

Articles