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A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method

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  • Murat Osmanoglu
  • Mustafa Bayram

Abstract

We have considered linear partial differential algebraic equations (LPDAEs) of the form Aut(t, x) + Buxx(t, x) + Cu(t, x) = f(t, x), which has at least one singular matrix of A, B ∈ ℝn×n. We have first introduced a uniform differential time index and a differential space index. The initial conditions and boundary conditions of the given system cannot be prescribed for all components of the solution vector u here. To overcome this, we introduced these indexes. Furthermore, differential transform method has been given to solve LPDAEs. We have applied this method to a test problem, and numerical solution of the problem has been compared with analytical solution.

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Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:705313
DOI: 10.1155/2013/705313
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