Bio-heat transfer is the study of external or internal heat transfer in the biological body. In different therapeutic treatments especially in cancer treatment, heat is used to cure infected cells. The required temperature that will kill the infected cell should be known before starting the thermal treatment on human tissue. The useful ways to measure the temperature distribution on human tissu...

In this paper, we consider a type of fractional diffusion equation (FDE) with variable coefficient on a finite domain. Firstly, we utilize a second-order scheme to approximate the Riemann-Liouville fractional derivative and present the finite difference scheme. Specifically, we discuss the Crank-Nicolson scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the...

We consider a model initial and boundary value problem for the wide-angle ‘parabolic’ equation Lur = icu of underwater acoustics, where L is a second-order differential operator in the depth variable z with depthand range-dependent coefficients. We discretize the problem by the Crank–Nicolson finite difference scheme and also by the forward Euler method using nonuniform partitions both in depth...

In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger’s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton’s explicit group iterative methods for a general Burger’s equation. The propo...

Systems of nonlinear partial differential equations modeling turbulent fluid flow and similar processes present special challanges in numerical analysis. Regions of stability of implicit-explicit methods are reviewed, and an energy norm based on Dahlquist’s concept of G-stability is developed. Using this norm, a time-stepping Crank-Nicolson Adams-Bashforth 2 implicit-explicit method for solving...

The nonlocal boundary value problem for Schrödinger equation in a Hilbert space is considered. The second-order of accuracy r-modified Crank-Nicolson difference schemes for the approximate solutions of this nonlocal boundary value problem are presented. The stability of these difference schemes is established. A numerical method is proposed for solving a one-dimensional nonlocal boundary value ...

The finite-difference time-domain (FDTD) method based on the iterated Crank–Nicolson (ICN) scheme is extended to a frequency-dependent version. Drude model used express metal dispersion, which incorporated into formulation with trapezoidal recursive convolution technique. validity of present convolutional perfectly matched layers discussed through analysis metal-insulator-metal plasmonic wavegu...

We present two unconditionally stable finite-difference time-domain (FDTD) methods for modeling the Sagnac effect in rotating optical microsensors. The methods are based on the implicit Crank-Nicolson scheme, adapted to hold in the rotating system reference frame-the rotating Crank-Nicolson (RCN) methods. The first method (RCN-2) is second order accurate in space whereas the second method (RCN-...