On numerical solution of third-order boundary-value problems. (English) Zbl 0727.65069
The equation \(y'''(x)=f(x)y(x)+g(x),\) \(a<x<b,\) with suitable boundary conditions at the points a and b is discretized by a fourth order method in the following way:
1. There is formed an exponential fitted difference scheme based on the exact solution of \(y'''(x)=\alpha^ 3y(x),\) \(a<x<b,\)
2. The exponential terms are substituted by several Padé approximants.
Properties of fourth order convergence are mentioned. Two numerical examples confirm the theoretical order results.
1. There is formed an exponential fitted difference scheme based on the exact solution of \(y'''(x)=\alpha^ 3y(x),\) \(a<x<b,\)
2. The exponential terms are substituted by several Padé approximants.
Properties of fourth order convergence are mentioned. Two numerical examples confirm the theoretical order results.
Reviewer: E.Pfeifer (Dresden)
MSC:
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 65L12 | Finite difference and finite volume methods for ordinary differential equations |
| 34B05 | Linear boundary value problems for ordinary differential equations |
Keywords:
third-order boundary-value problems; fourth order method; exponential fitted difference scheme; Padé approximants; fourth order convergence; numerical examplesReferences:
| [1] | The Numerical Treatment of Differential Equations, Springer-Verlag, Berlin, 1960. · doi:10.1007/978-3-642-88434-4 |
| [2] | The Numerical Solution of Two Point Boundary Value Problems in Ordinary Differential Equations, Oxford University Press, London, 1957. |
| [3] | Kreiss, Math. Comput. 26 pp 605– (1972) |
| [4] | Computational Methods in Engineering Boundary Value Problems, Academic Press, New York and London, 1979. · Zbl 0456.76002 |
| [5] | Usmani, J. Math. Phys. Sci. 18 pp 365– (1984) |
| [6] | Agarwal, J. Math. Phys. Sci. 8 pp 571– (1974) |
| [7] | Agarwal, J. Math. Phys. Sci. 12 pp 45– (1978) |
| [8] | Initial Value Methods for Boundary Value Problems, Academic Press, New York and London, 1973. |
| [9] | (ed), Numerical Solution of Ordinary and Partial Differential Equations, Addison-Wesley, Reading, Massachusetts, 1972. |
| [10] | Twizell, Int. j. numer. meth. eng. 23 pp 2089– (1986) |
| [11] | Twizell, Commun. appl. numer. meth. 4 pp 371– (1988) · Zbl 0627.73082 · doi:10.1002/cnm.1630040107 |
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