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

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