Abstract
The variational iteration method is applied to solve a class of nonlinear singular boundary value problems that arise in physiology. The process of the method, which produces solutions in terms of convergent series, is explained. The Lagrange multipliers needed to construct the correctional functional are found in terms of the exponential integral and Whittaker functions. The method easily overcomes the obstacle of singularities. Examples will be presented to test the method and compare it to other existing methods in order to confirm fast convergence and significant accuracy.
Highlights
In this paper, He’s variational iteration method (VIM) [1, 2] is applied to obtain an approximate solution for the following nonlinear singular two-point boundary value problem (BVP):pp (xx) yyy′ = pp (xx) ff xxx xx, 0 ≤ xx x xx (1)with the following two sets of boundary conditions: yyy (0) = 0, αααα (1) + βββββ (1) = γγγ (2)yy (0) = AAAAAAA (1) + βββββ (1) = γγγ (3)where pp (xx) = xxbbh (xx), xx x [0,1] . (4)Here αα α α, ββ β β, and AA and γγ are nite constants
It is assumed that pppppp is nonnegative, continuously differentiable on [0,1], and 1/h(xxx is analytic in the disk |zzz z zz for some rrrr
Assuming that xxxxxxxx is analytic in |zzz z zz for some rrrr, the existence-uniqueness has been established for problem (1) under the following restrictions: (1) BC (2) holds for αα αα, ββ ββ and such that bb bb, and (2) BC (3) holds for αα αα, ββ ββ, and such that 0 ≤ bb bb
Summary
He’s variational iteration method (VIM) [1, 2] is applied to obtain an approximate solution for the following nonlinear singular two-point boundary value problem (BVP):. Is problem arises in the study of a steady-state oxygen diffusion in a cell with Michaleis-Menten uptake kinetics when bb b b and h(xxxx x [6]. E objective of this paper is to apply the VIM to obtain an approximate solution for the proposed nonlinear singular boundary value problems with more relaxed pppppp. In case of linear differential equations, exact solution by the VIM can be readily obtained by a one iteration step because the exact Lagrange multiplier needed to construct the correctional functional can be identi ed
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