The variable order wave equation plays a major role in acoustics, electromagnetics, and fluid dynamics. In this paper, we consider the space-time variable order fractional wave equation with variable coefficients. We propose an effective numerical method for solving the aforementioned problem in a bounded domain. The shifted Jacobi polynomials are used as basis functions, and the variable-order...

Abstract In this manuscript, we implement a spectral collocation method to find the solution of reaction–diffusion equation with some initial and boundary conditions. We approximate by using two-dimensional interpolating polynomial dependent Legendre–Gauss–Lobatto points. fully show that achieved solutions are convergent exact when number points increases. demonstrate capability efficiency prov...

in this paper, an effective technique is proposed to determine thenumerical solution of nonlinear volterra-fredholm integralequations (vfies) which is based on interpolation by the hybrid ofradial basis functions (rbfs) including both inverse multiquadrics(imqs), hyperbolic secant (sechs) and strictly positive definitefunctions. zeros of the shifted legendre polynomial are used asthe collocatio...

Two solution algorithms are developed for the conditional moment closure (CMC) using quadrature-based methods (QBMM). Their primary purpose is to eliminate necessity of additional grid conditioning variable (e.g., mixture fraction). As in almost every probability-density-function (PDF)-based description, main technical hurdle molecular-mixing term. Here focus on solving this term coupled with c...

Several old and new finite-element preconditioners for nodal-based spectral discretizations of −∆u = f in the domain Ω = (−1, 1) (d = 2 or 3), with Dirichlet or Neumann boundary conditions, are considered and compared in terms of both condition number and computational efficiency. The computational domain covers the case of classical single-domain spectral approximations (see [5]), as well as t...

Lagrangian systems with ideal nonholonomic constraints can be expressed as implicit index 2 differential-algebraic equations (DAEs) and can be derived from the Lagrange-d’Alembert principle. We define a new nonholonomically constrained discrete Lagrange-d’Alembert principle based on a discrete Lagrange-d’Alembert principle for forced Lagrangian systems. Nonholonomic constraints are considered a...

An algorithm is described for the efficient numerical solution of singular two-point boundary value problems. The algorithm is based on collocation at Gauss points, is applied directly to second order equations and uses a transformation of the independent variable to obtain extra smoothness if needed. Numerical comparisons between a code based on this approach and codes based on other options w...