Mithun Bairagi | Searcharxiv

arXiv2023

A New Algorithm to determine Adomian Polynomials for nonlinear polynomial functions

We present a new algorithm by which the Adomian polynomials can be determined for scalar-valued nonlinear polynomial functional in a Hilbert space. This algorithm calculates the Adomian polynomials without the complicated operations such as parametrization, expansion, regrouping, differentiation, etc. The algorithm involves only some matrix operations. Because of the simplicity in the mathematical operations, the new algorithm is faster and more efficient than the other algorithms previously reported in the literature. We also implement the algorithm in the MATHEMATICA code. The computing speed and efficiency of the new algorithm are compared with some other algorithms in the one-dimensional case.

cs.CE↗

arXiv2022

GiNaCDE: the high-performance F-expansion and First Integral Methods with C++ library for solving Nonlinear Differential Equations

We present the algorithms for three popular methods: F-expansion, modified F-expansion, and first integral methods to automatically get closed-form traveling-wave solutions of nonlinear partial differential equations (NLPDEs). We generalize and improve the methods. The proposed algorithms are manageable, straightforward, and powerful tools providing a high-performance evaluation of the exact solutions of nonlinear ordinary differential equations (NLODEs) and NLPDEs. For differential equations with parameters, the new algorithms determine the conditions on the parameters to obtain exact solutions. The algorithms show solutions to a wide variety of NLODEs and NLPDEs, both integrable and non-integrable. It can solve NLODEs and NLPDEs that contain complex functions. The algorithms are implemented in a C++ library named GiNaCDE. The efficiency and effectiveness of the algorithms are demonstrated by some examples with the help of GiNaCDE. The output results tally with the previously known results, and in some cases, new exact traveling-wave solutions are explicitly obtained. Use of the library, implementation issues, scope, limitations, and future extensions of the software are addressed.

physics.comp-ph↗