Error estimates for a stiff differential equation procedure

A posteriori $ L^2(L^2)$-error estimates with the new version of streamline diffusion method for the wave equation

In this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. We prove a posteriori $ L^2(L^2)$ and error estimates for this method under minimal regularity hypothesis. Test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.

Regularization and New Error Estimates for a Modified Helmholtz Equation

We consider the following Cauchy problem for the Helmholtz equation with Dirichlet boundary conditions at x = 0 and x = π    ∆u− ku = 0, (x, y) ∈ (0, π)× (0, 1) u(0, y) = u(π, y) = 0, y ∈ (0, 1) uy(x, 0) = f(x), (x, y) ∈ (0, π)× (0, 1) u(x, 0) = φ(x), 0 < x < π (1) The problem is shown to be ill-posed, as the solution exhibits unstable dependence on the given data functions. Using a modifi...

A Cauchy Problem for Helmholtz Equation : Regularization and Error Estimates

In this paper, the Cauchy problem for the Helmholtz equation is investigated. It is known that such problem is severely ill-posed. We propose a new regularization method to solve it based on the solution given by the method of separation of variables. Error estimation and convergence analysis have been given. Finally, we present numerical results for several examples and show the effectiveness ...

A method for solving first order fuzzy differential equation

On Optimal Order Error Estimates for the Nonlinear Schrödinger Equation

Implicit Runge–Kutta methods in time are used in conjunction with the Galerkin method in space to generate stable and accurate approximations to solutions of the nonlinear (cubic) Schrödinger equation. The temporal component of the discretization error is shown to decrease at the classical rates in some important special cases.