On a finite difference analogue of a singular boundary value problem.
On numerical solution of a mildly nonlinear turning point problem
On Some Difference Schemes for Singular Singularly-Perturbed Boundary Value Problems.
One-dimensional adaptive grid generation.
Opposing flows in a one dimensional convection-diffusion problem
In this paper, we examine a particular class of singularly perturbed convection-diffusion problems with a discontinuous coefficient of the convective term. The presence of a discontinuous convective coefficient generates a solution which mimics flow moving in opposing directions either side of some flow source. A particular transmission condition is imposed to ensure that the differential operator is stable. A piecewise-uniform Shishkin mesh is combined with a monotone finite difference operator...
Parameter-uniform fitted mesh method for singularly perturbed delay differential equations with layer behavior.
Partitioned Adaptive Runge-Kutta Methods for the Solution of Nonstiff and Stiff Systems.
Partitioned Runge-Kutta Methods with Stiffness Detection and Stepsize Control.
Power bounded prolongations and Picard-Lindelöf iteration.
Some comparisons of difference schemes on meshes of Shishkin and Bakhvalov type.
Some remarks on an ODE-solver of Kirchgraber.
Special meshes and higher-order schemes for singularly perturbed boundary value problems.
The application of a class of one-step methods to solve the initial value problem
The Application of Rosenbrock-Wanner Type Methods with Stepsize Control in Differential-Algebraic Equations.
The h, p and h-p Versions of the Finite Element Method in 1 Dimension. Part II. The Error Analysis of the h- and h-p Versions.
The mesh chopping algorithm for singularly perturbed boundary value problem.
The method of normal splines for linear implicit differential equations of second order.
The structure of spline collocation matrix for singularly perturbation problems with two small parameters.
Toward a two-step Runge-Kutta code for nonstiff differential systems
Various issues related to the development of a new code for nonstiff differential equations are discussed. This code is based on two-step Runge-Kutta methods of order five and stage order five. Numerical experiments are presented which demonstrate that the new code is competitive with the Matlab ode45 program for all tolerances.
Two one-step methods to solve the initial value problem