Abstract
For the boundary value problem (BVP) of a second-order partial differential equation on a plane triangle area, we propose a new algorithm based on the Adomian decomposition method (ADM) combined with a segmented technique. In addition, we present a new theorem that ensures the convergence of the algorithm. By this algorithm, the model for the effect of regional recharge on the plane triangle groundwater flow region is solved, from which we obtain the segmented exact solution of the problem, which satisfies the governing equation and all of the specified boundary conditions. Then, by the algorithm combined with Taylor’s formula, the heterogeneous aquifer model on the plane triangle groundwater flow region is considered, from which we obtain the segmented high-precision approximate solution of the problem.
Highlights
Several different resolution techniques for solving boundary value problem (BVP) based on the Adomian decomposition method (ADM) were considered by Adomian [14], Rach, Wazwaz [15, 16], Dehghan [17, 18], Duan [19], and so on
For the boundary value problem of partial differential equations, the solution can be obtained by the ADM that satisfies all of the boundary conditions only with modification of the algorithm to accommodate the boundary
Adomian [20] first proposed an algorithm for boundary value problems of partial differential equations based on the ADM by taking the average of its two partial solutions
Summary
Many researchers have proposed and developed various techniques for solving partial differential equations such as Lie symmetry [1, 2], homotopy perturbation method [3, 4], homotopy analysis method [5, 6], the Adomian decomposition method (ADM) [7, 8], auxiliary equation methods [9, 10], variational iteration method [11,12,13], and so on.Among those methods, the Adomian decomposition method is a practical technique for solving (initial) boundary value problems for differential equations. Adomian [20] first proposed an algorithm for (initial) boundary value problems of partial differential equations based on the ADM by taking the average of its two partial solutions.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
