Non-iterative solution of a boundary value problem in reactor design by parameter differentiation

Abstract

In a recent paper, Shacham and Kehat[l] discuss the Department of Chemical Engineering, problem of solving a single non-linear algebraic equation.Unioersity of Edinburgh, They present the following convergence criteria (their King's Buildings, notation and equation numbers)-Mavfield Road.(Thus convergence is deemed to have occurred when two successive iterates are close together and bound the root.The authors state that criterion ( 15) is not used in the chemical engineering literature. It would appear that they may have overlooked two algorithms which make use of ( 15), namely the Rule of False Position[2] and Cox's method[3], both of which exhibit superlinear convergence [4] and have been successfully applied to chemical engineering problems [5,6].If the comparison of algorithms had included these two techniques the advantages of the authors' novel algorithms might have been demonstrated more clearly.