In this book a sixth-order parallel splitting method is developed to get more accurate numerical solution of Parabolic Partial Differential equations. Here sixth-order approximations for second-order parabolic partial differential equations and their algorithms are developed using six parallel processors. In addition to giving a more favorable truncation error, the use of higher order approximates to the matrix exponential functions improves the stability properties of finite difference schemes yielded, which is clear in examples and results are compared.