Solving Partial Differential Equations with Chaotic Asynchronous Schemes in Multi-Interaction Systems

Finite difference method for solving partial integro-differential equations

In this paper, we have introduced a new method for solving a class of the partial integro-differential equation with the singular kernel by using the finite difference method. First, we employing an algorithm for solving the problem based on the Crank-Nicholson scheme with given conditions. Furthermore, we discrete the singular integral for solving of the problem. Also, the numerical results ob...

Finite integration method for solving multi-dimensional partial differential equations

Based on the recently developed Finite Integration Method (FIM) for solving one-dimensional ordinary and partial differential equations, this paper extends the technique to higher dimensional partial differential equations. The main idea is to extend the first order finite integration matrices constructed by using either Ordinary Linear Approach (OLA) (uniform distribution of nodes) or Radial B...

Periodic Solutions of Chaotic Partial Differential Equations

Solving partial differential equations via sparse SDP

To solve a partial differential equation (PDE) numerically, we formulate it as a polynomial optimization problem (POP) by discretizing it via a finite difference approximation. The resulting POP satisfies a structured sparsity, which we can exploit to apply the sparse SDP relaxation of Waki, Kim, Kojima and Muramatsu [20] to the POP to obtain a roughly approximate solution of the PDE. To comput...

Solving a Class of Partial Differential Equations by Differential Transforms Method

‎In this work, we find the differential transforms of the functions $tan$ and‎ ‎$sec$‎, ‎and then we applied this transform on a class of partial differential equations involving $tan$ and‎ ‎$sec$‎.