Analytical solutions via coupled Elzaki adomian decomposition method for some applications

An efficient combination of Adomian Decomposition iterative technique coupled Elzaki transformation (ETADM) for solving Telegraph equation and Riccati non-linear differential equation (RNDE) is intrduced in a nvel way to gt an accurate analytical An efficient combination of Adomian o mian Decomposition o sition iteratvetechnique e technique cou led Elzaki transformation (ETADM) for solving Teleg aph equation and Riccati non-inear differential equation solution. An elegant combination of the Elzaki transform, the series expansion method, and (RNDE) is ntroduced in a n vel way to get an a curate anatical solution An ele ant combnation the Adomian i an polynomial. The suggested method will l convert differential equations into o e ak t sf h es p s n d Ad a p y i . T gge iterative algebraic equations, thus reducing processing and analytical work. The technique th dill t diff nil q tint it tiv lg b ic ti th d ci proces ing and analytical work Th te hnique soves the problem of calculating the Adomian solves the problem of calculating the Adomian polynomials. The method's efficiency was polynomials The method's efficiency was investigated usig some nuerical instances and the investigated using some numerical instances, and the findings n dings demonstrate m onstrate that it is easier findings demonstrate at t is easier to use than m ny other numerica procedurs. It has also been to use than many other th er numerical procedures. It has also been established that (ETADM) es a lished that (ETADM) is a trustworthy technique or solving ifferential equations. Using the is a trustworthy technique for solving differential equations. Using the Mathematica 13.3 3 3 p gr me, g p h pp o t re programme, the graphs of the approximate solutions are presented.