A Hybrid Scheme for Efficient Numerical Solution of the Fractional Telegraph Equation

Abstract

The paper presents a novel technique for solving the fractional telegraph equation (FTE) using a combination of the Chebyshev collocation method and finite difference scheme. FTE is a generalization of the classical telegraph equation and is widely used in many areas of physics and engineering. The proposed method combines the advantages of both Chebyshev collocation and finite difference schemes to provide accurate and efficient solutions. A detailed error analysis is carried out to investigate the convergence behavior of the scheme and is compared with other numerical methods. Examples are given to demonstrate the efficiency and accuracy of the method and highlight its potential for solving more complex problems. Overall, our results show that the combined method of Chebyshev collocation and finite difference is a potent tool for solving FTE, providing reliable and accurate solutions with excellent convergence rates.