Parallel LS-SVM for the numerical simulation of fractional Volterra’s population model

Abstract

In this paper, we develop a least-squares support vector machine (LS-SVM) for solving a nonlinear fractional-order Volterra’s population model in a closed system. The fractional rational Legendre functions with an orthogonal property on a semi-infinite domain have been used as the kernel of LS-SVM. Learning the solution is done by solving a non-linear constrained optimization problem. To accelerate the learning process, we propose two different approaches based on the orthogonality of kernels and a shared-memory task parallelization scheme for multi-core systems. By carrying out several experiments, it is seen that the proposed approaches provide accurate solutions for fractional-order Volterra’s population model.

Keywords

• Least squares support vector machine
• Volterra’s population model
• Fractional derivative
• Collocation LS-SVR
• Parallel algorithm