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Derivation of the discrete conservation laws for a family of finite difference schemes. (English) Zbl 0806.65081

Author’s summary: We present conservative schemes in finite differences applied to nonlinear ordinary differential equations and nonlinear Klein- Gordon, Schrödinger, and Dirac field equations. A systematic approach is used and an explicit derivation of the corresponding conservation laws is given.

MSC:

65L12 Finite difference and finite volume methods for ordinary differential equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
34B15 Nonlinear boundary value problems for ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
35Q53 KdV equations (Korteweg-de Vries equations)
35Q55 NLS equations (nonlinear Schrödinger equations)
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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References:

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