Monotone Difference Schemes for Singular Perturbation Problems
Copyright policy )Monotone Difference Schemes for Singular Perturbation Problems
We consider numerical solutions of the boundary value problem $\varepsilon y'' - (f(y))' - b(x,y) = 0$, $0 \leqq x \leqq 1$, $y(0) = A$, $y(1) = B$, $\varepsilon < 0$, $b_y \geqq \delta < 0$, with monotone difference schemes on nonuniform grids. We prove general convergence results and show that the Engquist–Osher monotone scheme will reproduce essential properties of the true solution for any grid. For the inversion of the nonlinear scheme, we suggest implicit time relaxation with variable time steps.
Numerical solution of boundary value problems involving ordinary differential equations, Newton's method, Nonlinear boundary value problems for ordinary differential equations, monotone difference schemes, singular perturbation problems, Mesh generation, refinement, and adaptive methods for ordinary differential equations
Numerical solution of boundary value problems involving ordinary differential equations, Newton's method, Nonlinear boundary value problems for ordinary differential equations, monotone difference schemes, singular perturbation problems, Mesh generation, refinement, and adaptive methods for ordinary differential equations
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