Approximate series solution of nonlinear singular boundary value problems arising in physiology.
We introduce an efficient recursive scheme based on Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems. This approach is based on a modification of the ADM; here we use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the solution components. In fact, we develop the recursive scheme without any undetermined coefficients while computing the solution components. Unlike the classical ADM, the proposed method avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. The uniqueness of the solution is discussed. The convergence and error analysis of the proposed method are also established. The accuracy and reliability of the proposed method are examined by four numerical examples.
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India.
Randhir
0000-0003-0283-3754
R
Singh
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India.
Jitendra
0000-0002-8065-7269
J
Kumar
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India.
Gnaneshwar
0000-0002-5247-9696
G
Nelakanti
D000465:Algorithms; D008962:Models, Theoretical