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Numerical methods for hyperbolic differential functional problems

Ciarski R.

Opuscula Mathematica

2008

Vol. 28, no. 1

29-46

The paper deals with the initial boundary value problem for quasilinear first order partial differential functional systems. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional systems are presented. The convergence results are proved by means of consistency and stability arguments. A numerical example is given.

Stability of difference equations generated by parabolic differential functional equations

Ciarski R.

Demonstratio Mathematica

2005

Vol. 38, nr 1

101--117

The aim of this paper is to present a numerical approximation for the initial boundary value problem for quasilinear parabolic differential functional equations. The convergence result is proved for the difference scheme with the property that the difference operators approximating mixed derivatives depend on local properties of coefficients of the differential equation. A numerical example is given.

Stability of difference equations generated by quasilinear differential functional problems

Ciarski R.

Demonstratio Mathematica

2002

Vol. 35, nr 3

557-571

The paper deals with the initial boundary value problem for quasilinear first order partial differential functional equations. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional equations are presented. The convergence results are proved by means of consistency and stability arguments. Numerical example is given.