Simulation of 13 points Laplacian operator in cylindrical mesh system by using explicit finite difference technique

Abstract

In nearest period of time a considerable and remarkable work have been done on the graphic design artificial intelligence, optimization, solving numerical approximation of ordinary as well as Partial differential equation by some differential operator, Discrete Laplacian operator is one of the most modern technique used for discretizatise the Ordinary differential equations (ODES) and Partial Differential equation (PDES). It is most simple technique, the researcher have taken great interest, as they may be able to find the novelty in their results specially in simulation of di-block co-polymer, solving the partial differential equation and also in finding light equation, wave equation in one as well as two dimension and etc. Discrete laplacian operator plays an essential role in the field of science and technology, shape interpolation, smoothing of the surface area, editing the meshes are the best usages of discrete laplacian operator In this study, a finite difference scheme is applied to develop the Laplacian operator using a cylindrical mesh system containing thirteen-point stencils. Laplacian operator has a significant role in the study of numerous mathematical and scientific phenomena. This employed in numerous significant computational and mathematical models, such as the Cell Dynamic Simulation system for the study of cutting-edge materials and image processing. The laplacian operator is necessary for being an isotropic discrete differential operator in a variety of models. When computing discrete isotropic results on curved surfaces, the curvilinear coordinate system may be a good option.