Two new second-order finite difference techniques based upon the classical 3-point backward time centered space (BTCS) method and the Crank–Nicolson scheme, and also a fourth-order finite difference scheme based on Crandall's method for one-dimensional diffusion, are used to solve the...

This work studies the inverse problem of reconstructing a time-dependent heat source in the heat conduction equation using the temperature measurement specified at an internal point. Problems of this type have important applications in several fields of applied science. By the Green’s function...

In this paper, we propose a new class of high-order accurate methods for solving the two-dimensional unsteady convection–diffusion equation. These techniques are based on the method of lines approach. We apply a compact finite difference approximation of fourth order for discretizing spatial...

The nonlinear sine-Gordon equation arises in various problems in science and engineering. In this paper, we propose a numerical scheme to solve the two-dimensional damped/undamped sine-Gordon equation. The proposed scheme is based on using collocation points and approximating the solution...

This study presents numerical schemes for solving two three-dimensional parabolic inverse problems. These schemes are developed for indentifying the parameter p(t) which satisfy ut=uxx+uyy+uzz+p(t)u+φ, in R×(0,T], u(x,y,z,0)=f(x,y,z),(x,y,z)∈R=[0,1]3. It is assumed that u is known on the...