Some new transfoms appear recently such as Sumudu, ELzaki and Aboodh transforms...etc. Of course with the well known Laplace transform.
Which one is highly recommended for nonlinear ODE\PDE and why?
Thanks
Sir all these transforms solve only linear problems like Laplace transform.By converting non linear problem into linear problem ( using any method like substitution method) we can solve non linear problem using these transforms.
Directly we can not solve non linear problems using these transforms (my point of view).
Solving nonlinear ordinary differential equations using the NDM
In this research paper, the authors examine a novel method called the Natural Decomposition Method (NDM). They use the NDM to obtain exact solutions for three different types of nonlinear ordinary differential equations (NLODEs). The NDM is based on the Natural transform method (NTM) and the Adomian decomposition method (ADM). By using the new method, they successfully handle some class of nonlinear ordinary differential equations in a simple and elegant way. The proposed method gives exact solutions in the form of a rapid convergence series. Hence, the Natural Decomposition Method (NDM) is an excellent mathematical tool for solving linear and nonlinear differential equation. One can conclude that the NDM is efficient and easy to use.
Article Solving nonlinear ordinary differential equations using the NDM
Other methods are ADM, LDM, SDM
A single transform like Laplace, Sumudu, Elzaki etc can not solve non linear problem. To solve this types of problem need extension in these transforms. See Wazwaz work.
Dear Aggarwal,
Many thanks for your response, if the Laplace Transform(LT) can solve linear ODE, why there are new transform? or what is the advantadge of introducing other transform? or what are the limitations of LT .
Best regards,
Majeed
Respected Majeed sir,
I am also searching the answer of same question. I asked the same question to all the authors who introduced the transforms Elzaki, Aboodh, Sumudu, Kamal, Mahgoub, Yang, Mohand etc . I know all the mention transforms are the extension of Laplace transform. But i am searching a problem which can not solve by Laplace but solve by theses transforms.
Differential transform and Natural transform decomposition methods are forms of transform (not integral transforms) methods that are used for solving nonlinear equations.
I will first recommend Classical Differential transform (DTM), DTM with PADE and Multi-step DTM. However, other methods includes HPM, VIM, VPM, VHPM, ADM, DJM etc.