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Numerical Solution of Ordinary Differential Equations
Abstract The initial value problem and the boundary value problem for the ordinary differential equations are discussed in this chapter. Derivation of simple numerical methods as well as a general approach for approximating formulas is described. The basic numerical methods applicable for open channel flow (i.e. for non-uniform grid) are developed. The problem of accuracy and stability including A-stability is discussed. Time integration of the systems of ordinary differential equations arising while solving the partial differential equations using the finite element method is described. A couple examples illustrating application of the presented methods for solving some typical problems of open channel hydraulics are included. At the end of chapter the shooting method and the difference method for solving the boundary value problem are presented.
Numerical Solution of Ordinary Differential Equations
Abstract The initial value problem and the boundary value problem for the ordinary differential equations are discussed in this chapter. Derivation of simple numerical methods as well as a general approach for approximating formulas is described. The basic numerical methods applicable for open channel flow (i.e. for non-uniform grid) are developed. The problem of accuracy and stability including A-stability is discussed. Time integration of the systems of ordinary differential equations arising while solving the partial differential equations using the finite element method is described. A couple examples illustrating application of the presented methods for solving some typical problems of open channel hydraulics are included. At the end of chapter the shooting method and the difference method for solving the boundary value problem are presented.
Numerical Solution of Ordinary Differential Equations
Szymkiewicz, Romuald (author)
2009-12-12
26 pages
Article/Chapter (Book)
Electronic Resource
English
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