A time-stepping DRBEM for nonlinear fractional sub-diffusion bio-heat ultrasonic wave propagation problems during electromagnetic radiation

Abstract

The main aim of this study is to develop a new DRBEM methodology for solving nonlinear fractional sub-diffusion bio-heat ultrasonic wave propagation problems during electromagnetic radiation. To remove domain integrals from the boundary integral equation, the DRBEM is employed. The Riemann–Liouville interpretation also discusses the time-fractional derivatives of concerns. The nonlinear, inhomogeneous, and temporal derivative terms were interpolated using the linear radial basis functions (RBFs). To attain high accuracy when solving nonlinear equations, we developed an implicit time-stepping scheme that dealt with the nonlinear term in each time step. DRBEM does not require mesh construction, making it appropriate for dealing with problems in complicated environments. Numerical results from the literature are used to demonstrate the correctness and utility of the proposed technique. The DRBEM technique and the FDM solution yield similar results. Our numerical findings further indicate the practicality of the proposed methodology.