Open AccessNumerical Method for 2D Quasi-linear Hyperbolic Equation on an Irrational Domain: Application to Telegraphic Equation
Author(s) -
Bishnu Pada Ghosh,
Nepal Chandra Roy
Publication year - 2021
Publication title -
the dhaka university journal of science
Language(s) - English
Resource type - Journals
eISSN - 2408-8528
pISSN - 1022-2502
DOI - 10.3329/dujs.v69i2.56492
Subject(s) - irrational number , mathematics , domain (mathematical analysis) , partial differential equation , hyperbolic partial differential equation , mathematical analysis , stability (learning theory) , space (punctuation) , geometry , computer science , machine learning , operating system
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)