Piece-wise continuous solution to a class of nonlinear boundary value problems

Abstract

In this paper, a new technique for solving a class of nonlinear Boundary Value Problems (BVPs) is introduced. Convergence of the series solution obtained from the proposed technique is proved. Convergence analysis is reliable enough to estimate the maximum absolute truncated error of the series solution. Some numerical examples are introduced to verify the efficiency of the new technique.

An accelerated solution for some classes of nonlinear partial differential equations

“…(2) or by El-Kalla formula [21], where the partial sum S n = n i=0 u i (x, t). For example, Table 1 shows the first four polynomials of the nonlinear term u 2 generated by both the traditional polynomials formula (7) and El-Kalla polynomials formula (8).…”

“…Clearly, the first four polynomials generated by El-Kalla formula (8) include the first four polynomials generated by the traditional formula (7) in addition to other terms that should appear in A 4 , A 5 , . .…”

Solution of a class of nonlinear differential equations using an accelerated version of Adomian decomposition method

“…Also, many modifications were made to this method by numerous researchers in an attempt to improve the accuracy or extend the applications of this method [1,2,6,11,19]. Also, El-Kalla polynomial was discussed by El-Kalla In [13,14,15,16,17,18], and conclude that El-kalla polynomial was directly used to estimate the maximum absolute truncated error of the Adomian series solution which cannot be estimated using the traditional polynomials.…”

Hybrid Cubic B-Spline Method for Solving Non-Linear Two-Point Boundary Value Problems

“…Nonlinear two-point boundary value problems have been solved approximately with shooting, finite difference, variational approach, Adomian decomposition, homotopy perturbation being amongst the more frequently used methods. Details on these methods as well as others can be found in [1,2,3,4,5,6,7,8,9,10,11,12,13].…”

“…Table 1 summarize some salient points (obtained from [1,2,3,4,5,6,7,8,9,10,11,12,13]) regarding some approximate methods.…”