A hybrid quantum-spectral-successive linearization method for general Lane–Emden type equations

This article presents a novel approach for solving the general Lane–Emden type equation with the quantum spectral method. This equation is a nonlinear initial value problem. We use a successive linearization to convert our problem to a linear system of equations, which is solved by a simple iteration method. This method is an iterative algorithm by combining quantum computing, pseudo-spectral, and successive linearization methods. In each iteration, we used a quantum algorithm and the final quantum state can be obtained by adding the quantum state in each iteration. Some numerical examples are considered and comparison with other existing methods, shows the efficiency of the method.