A nonstandard compact finite difference method for a truncated Bratu–Picard model

Abstract

In this paper, we used the nonstandard compact finite difference method to numerically solve one-dimensional truncated Bratu-Picard equations and discussed the convergence analysis of the proposed method. Depending on the parameters in the mentioned equation, it may have no solution, one solution, or two solutions; also, it may have infinitely many solutions. The numerical results show that our method covers all mentioned aspects depending on the parameters in the equation.

Keywords

• truncated bratu–picard model
• boundary value problems
• nonstandard compact finite difference methods