One of the most popular approaches to the numerical solution of two-point boundary value problems is shooting. However this approach is often ineffective for singularly perturbed problems due to the possible presence of rapidly increasing modes which cannot be dealt with using an initial value solve
Diagonally implicit runge-kutta formulae for the numerical integration of nonlinear two-point boundary value problems
β Scribed by J.R. Cash
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 1016 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0898-1221
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π SIMILAR VOLUMES
An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems wi',h periodic or oscillating solutions is developed in this paper. Numerical and theoretical results obtained for several well known problems show the efficiency of the new method. (~
## Abstract The integral equations arising from the Green's formula, applied to the twoβdimensional Helmholtz equation defined in a limited domain, are considered and the presence of instabilities in their numerical solution, when a real Green's function is adopted, is pointed out. A complete stud