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Green’s function and stability of a linear partial difference scheme. (English) Zbl 0907.39008

The authors study a linear partial difference equation which arises from discretizing heat and first order wave equations. An explicit formula for Green’s function of the equation is given. Various representation theorems, monotonicity, and oscillatory properties of Green’s function are obtained. Several stability criteria for arbitrary solutions are given. Numerical computations are provided for comparison with theoretical results.

MSC:

39A11 Stability of difference equations (MSC2000)
35K05 Heat equation
35L05 Wave equation
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65Q05 Numerical methods for functional equations (MSC2000)
39A12 Discrete version of topics in analysis
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References:

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