Third-order variable-mesh cubic spline methods for nonlinear two-point singularly perturbed boundary-value problems. (English) Zbl 0790.65073
Summary: A family of third-order variable-mesh methods for singularly perturbed two-point boundary value problems of the form \(\varepsilon y'' = f(x,y,y')\), \(y(a) = A\), \(y(b) = B\) is derived. The convergence analysis is given, and the method is shown to have third-order convergence properties. Several test examples are solved to demonstrate the efficiency of the method.
MSC:
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 65L12 | Finite difference and finite volume methods for ordinary differential equations |
| 65L50 | Mesh generation, refinement, and adaptive methods for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 34E15 | Singular perturbations for ordinary differential equations |
Keywords:
cubic splines; boundary layers; finite difference schemes; third-order variable-mesh methods; singularly perturbed two-point boundary value problems; third-order convergence; test examplesReferences:
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