Interpolation based numerical procedure for solving two-point nonlinear boundary value problems

Abstract

The present paper offers a simple, efficient and accurate straightforward numerical method for solving two-point nonlinear boundary value problems (NBVPs), which are frequently encountered in a broad discipline of sciences. The proposed technique is based on interpolation procedures and utilizes the capabilities of readily applicable functions, which are embedded in modern commercial mathematical software (Mathematica). The whole approach is computationally effortless, does not contain the drawbacks of other existing methods related to the solution of NBVPs and under the restriction of a sufficient guess of the interpolation domains is capable of tackling a variety of such problems, originated from different scientific areas. Several applications of the method produce results in excellent agreement with existing ones of the relevant literature, the latter being the product of far more sophisticated algorithms.