A fourth-order compact finite-difference scheme for solving a 1-D Pennes' bioheat transfer equation in a triple-layered skin structure

In this study, we develop a fourth-order compact finite-difference scheme for solving the 1-D Pennes' bioheat transfer equation in a triple-layered skin structure. To this end, we employ the fourth-order compact finite-difference method and the Crank-Nicholson method to discretize the Pennes' bioheat equation, where the second-order derivative of temperature, theta(xx), at boundaries and interfaces is calculated using a combined compact finite-difference method incorporating the boundary conditions and interfacial conditions. As such, the solution system becomes a diagonal-dominated tridiagonal linear system. The method is illustrated by two numerical examples.