Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 3 1 2022 02 01 Numerical differential continuation approach for systems of nonlinear equations with singular Jacobian 53 58 4644 10.22060/ajmc.2021.20487.1068 EN Mohammad Ali Mehrpouya Department of Mathematics, Tafresh University, 39518-79611, Tafresh, Iran Journal Article 2021 08 29  It is well known that, one of the useful and rapid methods for a nonlinear system of algebraic equations is Newton’s method. Newton’s method has at least quadratic convergence when the Jacobian is a nonsingular matrix in a neighborhood of the solution. In this paper, a differential continuation method is presented for solving the nonlinear system of algebraic equations whose Jacobian matrix is singular at the solution. For this purpose, at first, an auxiliary equation named the homotopy equation is constructed. Then, by differentiating from the homotopy equation, a system of differential equations is replaced instead of the target problem and solved. In other words, the solution of the nonlinear system of algebraic equations with singular Jacobian is transformed to the solution of a system of differential equations. Some numerical tests are presented at the end and the computational efficiency of the method is described. https://ajmc.aut.ac.ir/article_4644_e50683530c29d7c11727aae79307a397.pdf