Evaluation of branching points for nonlinear boundary-value problems based on the GPM technique
A novel general direct iteration algorithm for the evaluation of branching points of nonlinear boundary-value problems is suggested. The method proposed takes advantage of the GPM concept. The analysis presented in the paper encompasses also the determination of branching points in nonlinear algebraic equations. The method can be applied to problems arising in a number of physical and mathematical applications. The technique is tailored to problems of diffusion and heat conduction accompanied by a chemical reaction.