Partial Differential Equations (PDEs) play a very significant role in the life of scientists and engineers who wish to model complex physical processes. However, standard solutions to math have a hard time striking the correct balance of accuracy, stability, and the speed at which they can be of their tasks. In this research, it is proposed that new numeric techniques can be used to solve PDEs at a fast rate, higher convergence rates and reduced costs of computing. The new techniques utilise a better summability and flexible discretisation to provide a large variety of border cases and nonlinearities. Most computer experiments demonstrate that the proposed methods are faster and more precise compared to alternative approaches to the standard PDE problems. It is now possible to have fluid dynamics, heat movement, and electromagnetism models that are more precise. The study demonstrates that big computer systems may be able to use scalable application.