Related papers: A new semi-analytical approach for numerical solvi…
This work presents a brief discussion and a plan towards the analytical solving of Partial Differential Equations (PDEs) using symbolic computing, as well as an implementation of part of this plan as the PDEtools software-package of…
We propose an approach to solve the stochastic neutron point kinetics equations using an adaptation of the diagonalization-decomposition method (DDM). This new approach (Double-DDM) yields a nonstiff solution for the stochastic formulation,…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
A general class of KdV-type wave equations regularized with a convolution-type nonlocality in space is considered. The class differs from the class of the nonlinear nonlocal unidirectional wave equations previously studied by the addition…
Discrete Differential Equations (DDEs) are functional equations that relate polynomially a power series $F(t,u)$ in $t$ with polynomial coefficients in a "catalytic" variable $u$ and the specializations, say at $u=1$, of $F(t,u)$ and of…
This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…
Ensuring the safe and reliable operation of integrated electricity and gas systems (IEGS) requires dynamic energy flow (DEF) simulation tools that achieve high accuracy and computational efficiency. However, the inherent strong nonlinearity…
In this paper we construct high order numerical methods for solving third and fourth orders nonlinear functional differential equations (FDE). They are based on the discretization of iterative methods on continuous level with the use of the…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
In this work, an exact solution to a new generalized nonlinear KdV partial differential equations has been investigated using homotopy analysis techniques. The mentioned partial differential equation has been solved using homotopy…
Finite-difference time-domain (FDTD) is an effective algorithm for resolving Maxwell equations directly in time domain. Although FDTD has obtained sufficient development, there still exists some improvement space for it, such as…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
Nonlinear partial differential equations (PDEs) are crucial for modeling complex fluid dynamics and are foundational to many computational fluid dynamics (CFD) applications. However, solving these nonlinear PDEs is challenging due to the…
In this paper we discuss some issues that arise in the process of writing a fractional differential equation (FDE) by replacing an integer order derivative by a fractional order derivative in a given differential equation. To address these…
In this study, a fast multipole method (FMM) is used to decrease the computational time of a fully-coupled poroelastic hydraulic fracture model with a controllable effect on its accuracy. The hydraulic fracture model is based on the…
The Finite-Difference Time-Domain (FDTD) method is a well-known technique for the analysis of quantum devices. It solves a discretized Schrodinger equation in an explicitly iterative process. However, the method requires the spatial grid…
The paper derives an equation for the Cauchy transform of the solution of a free stochastic differential equation (SDE). This new equation is used to solve several particular examples of free SDEs.
We solve the Cauchy problem defined by the fractional partial differential equation $[\partial_{tt}-\kappa\mathbb{D}]u=0$, with $\mathbb{D}$ the pseudo-differential Riesz operator of first order, and the initial conditions…