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, θ 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.