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

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 Modied Picard's Method (VMP) method to get the convergent series solution.These suggested schemes give analytical approximation in an innite series form without using discretization.These methods are eectual and reliable which is demonstrated through six model problems having variety of source terms and analytic initial data.

Vectorial reduced differential transform method for fractional Cauchy–Riemann system of equations

“…They related this instability to CR system that's why the initial value problem for CR system is well known to be ill‐posed. Different fractional models discussed in References 12‐20 and the references mentioned therein. Some latest contributions covering different physical happenings are addressed in References 21‐27.…”