APPROXIMATE METHODS FOR THE INTEGRATION OF SINGULAR PERTURBATION PROBLEMS

Reliable Finite Element Methods for Self-adjoint Singular Perturbation Problems

It is well known that the standard finite element method based on the space Vh of continuous piecewise linear functions is not reliable in solving singular perturbation problems. It is also known that the solution of a two-point boundary-value singular perturbation problem admits a decomposition into a regular part and a finite linear combination of explicit singular functions. Taking into acco...

Boundary Layer Resolving Pseudospectral Methods for Singular Perturbation Problems

Pseudospectral methods are investigated for singularly perturbed boundary value problems for ordinary diierential equations which possess boundary layers. It is well known that if the boundary layer is very small then a very large number of spectral collocation points is required to obtain accurate solutions. We introduce here a new eeective procedure, based on coordinate stretching and the Che...

On the Convergence of Continuous-Time Waveform Relaxation Methods for Singular Perturbation Initial Value Problems

Variable Step/Order Generalized Upwind Methods for the Numerical Solution of Second Order Singular Perturbation Problems

We propose a simple and quite efficient code to solve singular perturbation problems when the perturbation parameter ǫ is very small. The code is based on generalized upwind methods of order ranging from 4 to 10 and uses highly variable stepsize to fit the boundary regions with relatively few points. An extensive numerical test section shows the effectiveness of the proposed technique on linear...

Numerical Integration Scheme Using Singular Perturbation Method

Some multi degree-of-freedom dynamical systems exhibit a response that contain fast and slow variables. An example of such systems is a multibody system with rigid and deformable bodies. Standard numerical integration of the resultant equations of motion must adjust the time step according to the frequency of the fastest variable. As a result, the computation time is sacrificed. The singular pe...