Abstract
In this paper, a numerical solution of partial differential-algebraic equations (PDAEs) is considered by multivariate Pade approximations. We applied this method to an example. First, PDAE has been converted to power series by two-dimensional differential transformation, and then the numerical solution of the equation was put into a multivariate Pade series form. Thus, we obtained the numerical solution of PDAEs.
Highlights
In this study, we consider linear partial differential-algebraic equations (PDAEs) of the formAut(t, x) + Buxx(t, x) + Cu(t, x) = f (t, x), ( )where t ∈ (, te) and x ∈ (–l, l) ⊂ R, A, B, C ∈ Rn,xn are constant matrices, u, f : [, te] × [–l, l] → Rn
Many important mathematical models can be expressed in terms of PDAEs
Much research has been focused on the numerical solution of PDAEs [, ]
Summary
1 Introduction In this study, we consider linear partial differential-algebraic equations (PDAEs) of the form The two special cases A = or B = lead to ordinary differential equations or DAEs which are not considered here. Much research has been focused on the numerical solution of PDAEs [ , ]. The purpose of this paper is to consider the numerical solution of PDAEs by using multivariate Padé approximations.
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