International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2528

Full Length Research Paper

Vectorial reduced differential transform (VRDT) method for the solution of inhomogeneous Cauchy-Riemann system

Tahir Naseem
  • Tahir Naseem
  • Department of Mathematics, HITEC University, Taxila Cantonment, Pakistan.
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Muhammad Tahir
  • Muhammad Tahir
  • Department of Mathematics, HITEC University, Taxila Cantonment, Pakistan.
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  •  Accepted: 27 January 2014
  •  Published: 30 January 2014

Abstract

It is well known that initial-value problem for the Cauchy-Riemann system is ill-posed and the problem with such Hadamard instability cannot be solved unless the initial data are analytic. In this paper, we present the vectorial reduced differential transform (VRDT) method to solve initial-value problem for the inhomogeneous Cauchy-Riemann system with analytic data. The VRDTM solution vector achieved is in the form of infinite series whose compact form is in agreement with the exact solution vector.

Key words: Inhomogeneous Cauchy-Riemann system, initial-value problem, vectorial reduced differential transform.