A numerical verification of solutionsof free boundary problems

Rigorous Shadowing of Numerical Solutionsof

An exact trajectory of a dynamical system lying close to a numerical trajectory is called a shadow. We present a general-purpose method for proving the existence of nite-time shadows of numerical ODE integrations of arbitrary dimension in which some measure of hyperbolicity is present and there is either 0 or 1 expanding modes, or 0 or 1 contracting modes. Much of the rigor is provided automati...

‎A Consistent and Accurate Numerical Method for Approximate Numerical Solution of Two Point Boundary Value Problems

In this article we have proposed an accurate finite difference method for approximate numerical solution of second order boundary value problem with Dirichlet boundary conditions. There are numerous numerical methods for solving these boundary value problems. Some these methods are more efficient and accurate than others with some advantages and disadvantages. The results in experiment on model...

Fast Numerical Methods for Bernoulli Free Boundary Problems

The numerical solution of the free boundary Bernoulli problem is addressed. An iterative method based on a level-set formulation and boundary element method is proposed. Issues related to the implementation, the accuracy and the generality of the method are discussed. The efficiency of the approach is illustrated by numerical results.

Numerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev Wavelets

In this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra  integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on wavelets, then we apply the Chebyshev wavelets to solve the integral equation. Numerical implementation of the method is illustrated by two ben...

On Free Boundary Problems