In this paper, we construct the new integral representation of Jost solution Sturm-Liouville equation with impuls in semi axis $[0,+\infty )$ and give type relation, examine properties Kernel function their partial derivatives $x$ $\ t$, constructed obtain differential provided by function. Finally, paper prove uniqueness determination potential scattering data.

In this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. A numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. Truncation errors are derived for both continuous and discontinuous problems. Parameter uni...

In this paper, we study the superconvergence of the error for the local discontinuous Galerkin (LDG) finite element method for one-dimensional linear parabolic equations when alternating flux is used. We prove that if we apply piecewise k-th degree polynomials, the error between the LDG solution and the exact solution is (k + 2)-th order superconvergent at the Radau points with suitable initial...

Convolving the output of Discontinuous Galerkin (DG) computations using spline filters can improve both smoothness and accuracy of the output. At domain boundaries, these filters have to be one-sided for non-periodic boundary conditions. Recently, position-dependent smoothness-increasing accuracy-preserving (PSIAC) filters were shown to be a superset of the well-known one-sided RLKV and SRV fil...

In this paper, we study the local discontinuous Galerkin (LDG) finite element method for solving a nonlinear Burger’s equation with Dirichlet boundary conditions. Based on the Hopf–Cole transformation, we transform the original problem into a linear heat equation with Neumann boundary conditions. The heat equation is then solved by the LDG finite element method with special chosen numerical flu...