In this research, we investigate the Laplace-Differential Transform method (LDTM) for solving the non-linear Reaction-Diffusion equation and provide our findings for both exact and approximation solutions as well as numerical solutions. In the time domain, we use the Laplace transform, and in the spatial domain, we use the differential transform with initial and boundary conditions. Unlike conventional methods, which typically include integration, we discover that this approach only necessitates straightforward differentiation and a few elementary operations for the result. The computational domain can be considerably reduced with this strategy, and only a small number of iterations are needed to provide closed-form answers in the form of series expansions of certain known functions. Numerous examples are provided to illustrate the technique's usefulness and effectiveness. Conclusions are reliable, and the computational effort required was less than that of some prior investigations.

Laplace differential transform method, Reaction diffusion equation