We describe a novel discretisation method for numerically solving (systems of) semilinear parabolic equations on Euclidean spheres. The new approximation method is based upon a discretisation in space using spherical basis functions and can be of arbitrary order. This, together with the fact that the solutions of semilinear parabolic problems are known to be infinitely smooth, at least locally ...

This paper deals with a monotone weighted average iterative method for solving semilinear singularly perturbed parabolic problems. Monotone sequences, based on the accelerated monotone iterative method, are constructed for a nonlinear difference scheme which approximates the semilinear parabolic problem. This monotone convergence leads to the existence-uniqueness theorem. An analysis of uniform...

‎In this paper‎, ‎a numerical procedure for an inverse problem of‎ ‎simultaneously determining an unknown coefficient in a semilinear ‎parabolic equation subject to the specification of the solution at‎ ‎an internal point along with the usual initial boundary conditions ‎is considered‎. ‎The method consists of expanding the required‎ ‎approximate solution as the elements of the inverse quadrati...

‎in this paper‎, ‎a numerical procedure for an inverse problem of‎ ‎simultaneously determining an unknown coefficient in a semilinear ‎parabolic equation subject to the specification of the solution at‎ ‎an internal point along with the usual initial boundary conditions ‎is considered‎. ‎the method consists of expanding the required‎ ‎approximate solution as the elements of the inverse quadrati...

    In this paper, a variational iteration method (VIM), which is a well-known method for solving nonlinear equations, has been employed to solve an inverse parabolic partial differential equation. Inverse problems in partial differential equations can be used to model many real problems in engineering and other physical sciences. The VIM is to construct correction functional using general Lagr...

In this paper we study the blow-up phenomenon for nonnegative solutions to the following parabolic problem: ut(x, t) = ∆u(x, t) + (u(x, t)) , in Ω× (0, T ), where 0 < p− = min p ≤ p(x) ≤ max p = p+ is a smooth bounded function. After discussing existence and uniqueness we characterize the critical exponents for this problem. We prove that there are solutions with blow-up in finite time if and o...