Local Partial Differential Algebra

Exact Solution for Nonlinear Local Fractional Partial Differential Equations

In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples a...

Numerical studies of non-local hyperbolic partial differential equations using collocation methods

The non-local hyperbolic partial differential equations have many applications in sciences and engineering. A collocation finite element approach based on exponential cubic B-spline and quintic B-spline are presented for the numerical solution of the wave equation subject to nonlocal boundary condition. Von Neumann stability analysis is used to analyze the proposed methods. The efficiency, accu...

A Partial-differential Approximation for Spatial Stochastic Process Algebra

We study a spatial framework for process algebra with ordinary differential equation (ODE) semantics. We consider an explicit mobility model over a 2D lattice where processes may walk to neighbouring regions independently, and interact with each other when they are in same region. The ODE system size will grow linearly with the number of regions, hindering the analysis in practice. Assuming an ...

Numerical Linear Algebra and Solvability of Partial Differential Equations

Differential Algebra

There are two main topics we will discuss in these lectures: (I) The core differential algebra: (a) Introduction: We will begin with an introduction to differential algebraic structures, important terms and notation, and a general background needed for this lecture. (b) Differential elimination: Given a system of polynomial partial differential equations (PDE’s for short), we will determine if ...