In this paper, we will solve the Logistic and Riccati di¤erential equations using VIM, shifted Chebyshev-spectral fourth kind methods and Hermite collocation method. Where we can from the numerical results we obtained to conclude that the solution using these three approaches converge to the exact solution is excellent. We note that we can apply the proposed methods to solve other problems in e...

A spectral collocation method is proposed to solve Volterra or Fredholm integral equations with weakly singular kernels and corresponding integro-differential equations by virtue of some identities. For a class of functions that satisfy certain regularity conditions on a bounded domain, we obtain geometric or supergeometric convergence rate for both types of equations. Numerical results confirm...

This paper studies the stochastic Burgers equation with moving boundaries. The solution is obtained numerically by employing differentiation matrices which are derived from spectral collocation. The stochastic term is considered only to be timedependent. It is argued that the solely time-dependent stochastic term does not create considerable amount of perturbation in the wave profile between th...

Preserving in the discrete realm the underlying geometric, topological, and algebraic structures at stake in partial differential equations has proven to be a fruitful guiding principle for numerical methods in a variety of fields such as elasticity, electromagnetism, or fluid mechanics. However, structure-preserving methods have traditionally used spaces of piecewise polynomial basis functions...

This work deals with the H1 condition numbers and the distribution of the ~ N;Msingular values of the preconditioned operators f~ 1 N;M WN;M ÂN;Mg. ÂN;M is the matrix representation of the Legendre Spectral Collocation discretization of the elliptic operator A de ned by Au := u + a1ux + a2uy + a0u in (the unit square) with boundary conditions: u = 0 on 0; @u @ A = u on 1. ~ N;M is the sti ness ...