Hyperbolic Heat Equation in Bar and Finite Difference Schemes of Exact Spectrum

摘要

The solutions of corresponding 1-D initial-boundary value problem and inverse problem for hyperbolic heat conduction equation are obtained numerically, using for the approach differential equations, the discretization in space applying the finite difference method and the best scheme with exact spectrum (BSES). Numerical solutions in the time are obtained by the MATLAB solver using the method of conjugate operators and the method of superposition. For finite difference approximation with central differences, strong numerical oscillations are presented, when the initial and boundary conditions are discontinuous for the problem. The method of BSES is without oscillations and this is effective way for numerical solutions.