Exploring fractional order 2-D Helmholtz equation using finite difference scheme through the bat optimization algorithm

This endeavor proposes an effective implementation of a hybrid technique for computing the approximate solution of fractional order Helmholtz equation, with Dirichlet boundary conditions. The novel scheme is an amalgamation of the traditional finite difference method with the bat optimization algorithm (BOA). This nature-inspired optimization technique simulates the echolocation behavior of foraging bats, which ascertain the surroundings through the echo of their emitted sound pulse. Systematically, the deliberated fractional order system is altered into an integer order partial differential equation by virtue of linearized expansion of Laplace transformation. Subsequently, the attained system is processed through the proposed innovative finite difference optimization technique (FDOT) the numerical discussions. Furthermore, some experiments are carried out in order to expound the effective execution and application of the technique. In addition, the convergence and accuracy of the scheme are also delineated numerically, via statistical inference. The significant outcomes of the analysis reveal the advantageousness of the proposed numerical scheme, which can efficiently handle the complexities of the fractional order 2-D Helmholtz equation.

Automated summary

This study introduces a hybrid technique combining the traditional finite difference method with the bat optimization algorithm to solve the fractional order Helmholtz equation effectively. The numerical experiments demonstrate the efficacy and accuracy of this novel approach in handling the complexities of the fractional order 2-D Helmholtz equation.