Physical Problems with Discontinuous Initial Conditions

Discontinuous Parabolic Problems with a Nonlocal Initial Condition

Let Ω be a an open bounded domain in R , N ≥ 2, with a smooth boundary ∂Ω. Let QT Ω × 0, T and ΓT ∂Ω × 0, T where T is a positive real number. Then ΓT is smooth and any point on ΓT satisfies the inside and outside strong sphere property see 1 . For u : QT → R we denote its partial derivatives in the distributional sense when they exist byDtu ∂u/∂t, Diu ∂u/∂xi,DiDju ∂u/∂xi∂xj , i, j 1, . . . ,N....

Eigenvalues of Sturm-liouville Problems with Discontinuous Boundary Conditions

For classical regular two-point self-adjoint Sturm-Liouville problems (SLP) the dependence of the eigenvalues on the boundary conditions is well understood because of some surprisingly recent results. Recently there has been a lot of interest in problems with discontinuous boundary conditions. Such conditions are known by various names including transmission conditions, interface conditions, po...

Pseudospectral vs. Finite Difference Methods for Initial Value Problems with Discontinuous Coefficient

An initial value problem with piecewise constant coefficients is considered. The accuracies for both finite difference methods and the pseudospectral method are analyzed, and a modification of the initial value problem is suggested. The modified problem is shown to have the same temporal period as the original problem does, and a second order accuracy is obtained for the pseudospectral method a...

Pseudospectral vs Finite Di erence Methods for Initial Value Problems with Discontinuous Coe cients

An initial value problem with piecewise constant coe cients is considered. The accuracies for both nite di erence methods and the pseudospectral method are analyzed, and a modi cation of the initial value problem is suggested. The modi ed problem is shown to have the same temporal period as the original problem does, and a second order accuracy is obtained for the pseudospectral method at integ...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation