#6620. On an approximate solution of a boundary value problem for a nonlinear integro-differential equation

November 2026publication date
Proposal available till 21-05-2025
4 total number of authors per manuscript0 $

The title of the journal is available only for the authors who have already paid for
Journal’s subject area:
Mathematics (all);
Agricultural and Biological Sciences (all);
Environmental Science (all);
Energy (all);
Biochemistry, Genetics and Molecular Biology (all);
Chemistry (all);
Materials Science (all);
Places in the authors’ list:
place 1place 2place 3place 4
FreeFreeFreeFree
2350 $1200 $1050 $900 $
Contract №6620.1 Contract №6620.2 Contract №6620.3 Contract №6620.4
1 place - free (for sale)
2 place - free (for sale)
3 place - free (for sale)
4 place - free (for sale)

Abstract:
The aim of this work is to discuss the solvability of a boundary value problem for a nonlinear integro-differential equation. First, we derive an equivalent nonlinear Fredholm integral equation (NFIE) to this problem. Second, we prove the existence of a solution to the NFIE using the Krasnosel’skii fixed point theorem under verifying some sufficient conditions. Third, we solve the NFIE numerically and study the convergence rate via methods based upon applying the modified Adomian decomposition method and Liao’s homotopy analysis method. As applications, some examples are illustrated to support our work. The results in this work refer to both methods are efficient and converge rapidly, but the homotopy analysis method may converge faster when we succeed in choosing the optimal homotopy control parameter.
Keywords:
Boundary value problem; existence; homotopy analysis method; integro-differential equations; modified Adomian’s decomposition method; uniqueness

Contacts :
0