Numerical determination of bounded solutions to discrete singularly perturbed equations and critical combustion regimes

Bounded on the entire axis, solutions to systems of singularly perturbed ordinary differential equations of fixed or high orders are found approximately. Finite-difference discretizations of the problems are studied. A priori estimates for the derivatives of solutions to the continuous and discrete problems and the relevant error estimates are proved. Numerical algorithms are constructed, and their convergence is analyzed. The results are applied to the problem of determining the critical parameter values in a mathematical combustion model.