A Complete Procedure for a Constraint-Type Fictitious Time Integration Method to Solve Nonlinear Multi-Dimensional Elliptic Partial Differential Equations

In this paper, an efficient and straightforward numerical procedure is constructed to solve multi-dimensional linear nonlinear elliptic partial differential equations (PDEs). Although the for constraint-type fictitious time integration method overcomes stability problem, parameter’s definition, accuracy computational efficiency have not been resolved, lack of initial guess values results in reduced efficiency. Therefore, normalized two-point boundary value solution Lie-group shooting proposed considered avoid problem value. Then, a space-time variable, including minimal step convergence rate factor, introduced study relationship between factor. Some benchmark examples are tested. As show, using can significantly converge within one step, better than that demonstrated previous literature.