Novel Schemes for Cauchy-Riemann System of Equations with Cauchy Conditions

Year 2021, Volume: 5 Issue: 1, 94 - 126, 31.03.2021

Tahir Naseem Muhammad Sohail , Hajra Zeb

https://doi.org/10.31197/atnaa.828790

Abstract

This communication deals with the analytical solutions of Cauchy problem for Cauchy-Riemann system of equations which is basically unstable according to Hadamard but its solution exists if its initial data is analytic. Here we used the Vectorial Adomian Decomposition (VAD) method, Vectorial Variational Iteration (VVI) method, and Vectorial Modified Picard’s Method (VMP) method to get the convergent series solution. These suggested schemes give analytical approximation in an infinite series form without using discretization. These methods are effectual and reliable which is demonstrated through six model problems having variety of source terms and analytic initial data.

Keywords

Cauchy-Riemann system of equations;, Cauchy problem;, Vectorial Adomian Decomposition method, Vectorial Variational Iteration method, Vectorial Modified Picard’s Method.

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