An efficient iterative technique for solving initial value problem for multidimensional partial differential equations
For researchers solving high-dimensional PDEs, this offers a potentially more efficient iterative method, but the contribution appears incremental as it builds on existing iterative approaches.
The paper presents a new iterative technique for solving initial value problems for multidimensional linear and nonlinear PDEs that avoids discretization, linearization, or small perturbations, significantly reducing numerical computations. Numerical examples for heat and wave equations demonstrate reliability, but no concrete performance numbers are given.
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization, linearization or small perturbations and therefore significantly reduces numerical computations. Rigorous convergence analysis of presented technique and an error estimate are included as well. Several numerical examples for high dimensional initial value problem for heat and wave type partial differential equations are presented to demonstrate reliability and performance of proposed iterative scheme.