相关论文: Dynamically Consistent Approximate Rational Soluti…
Our main objective in this paper is to develop a second-order stochastic numerical method which generalizes the well-known deterministic TR-BDF2 scheme. Since most stochastic techniques used for approximating the solution of a stochastic…
This paper develops a two-level fourth-order scheme for solving time-fractional convection-diffusion-reaction equation with variable coefficients subjected to suitable initial and boundary conditions. The basis properties of the new…
Functional Differential Equations (FDEs) play a fundamental role in many areas of mathematical physics, including fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equation), and statistical…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
In this work, we present a second-order numerical scheme to address the solution of optimal control problems constrained by the evolution of nonlinear Fokker-Planck equations arising from socio-economic dynamics. In order to design an…
This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite…
This work is devoted to the study of the nonlinear second-order neutral difference equations with quasi-differences of the form $$ \Delta \left( r_{n} \Delta \left( x_{n}+q_{n}x_{n-\tau}\right)\right)= a_{n}f(x_{n-\sigma})+b_n%, \ n\geq n_0…
Novel multi-step predictor-corrector numerical schemes have been derived for approximating decoupled forward-backward stochastic differential equations (FBSDEs). The stability and high order rate of convergence of the schemes are rigorously…
The solutions of fractional differential equations (FDEs) have a natural singularity at the initial point. The accuracy of their numerical solutions is lower than the accuracy of the numerical solutions of FDEs whose solutions are…
In this paper we consider the numerical solution of Fractional Differential Equations by means of $m$-step recursions. The construction of such formulas can be obtained in many ways. Here we study a technique based on the rational…
Properties of confined mesoscopic systems have been extensively studied numerically over recent years. We discuss an analytical approach to the study of finite rotating fermionic systems in two dimension. We first construct the energy…
Multiphysics systems are driven by multiple processes acting simultaneously, and their simulation leads to partitioned systems of differential equations. This paper studies the solution of partitioned systems of differential equations using…
This report addresses the boundary value problem for a second-order linear singularly perturbed FIDE. Traditional methods for solving these equations often face stability issues when dealing with small perturbation parameters. We propose an…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on our previous results concerning asymptotic solutions for large spring constant (or small angle of attack), we construct…
Efficient long-time integration of nonlinear fractional differential equations is significantly challenging due to the integro-differential nature of the fractional operators. In addition, the inherent non-smoothness introduced by the…
We obtained steady solutions to the two-dimensional Boussinesq approximation equations without mean temperature gradient. This system is referred to as free convection in this paper. Under an external flow described by the stream function…
Von Neumann established that discretized algebraic equations must be consistent with the differential equations, and must be stable in order to obtain convergent numerical solutions for the given differential equations. The "stability" is…
In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…
We obtain new exact classes of solutions for the nonlinear fractional Fokker-Planck-like equation partial_t rho = partial_x{D(x) partial^{mu -1}_x rho^{nu} - F(x) rho} by considering a diffusion coefficient D = D|x|^{-theta} (theta in R and…