Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24493120220201Numerical differential continuation approach for systems of nonlinear equations with singular Jacobian5358464410.22060/ajmc.2021.20487.1068ENMohammad AliMehrpouyaDepartment of Mathematics, Tafresh University0000-0001-9598-4943Journal Article20210829It is well known that, one of the useful and rapid methods for a nonlinear<br /><br />system of algebraic equations is Newton's method. Newton's method has at least<br /><br />quadratic convergence when the Jacobian is a nonsingular matrix in a neighborhood<br /><br />of the solution. In this paper, a differential continuation method is presented for<br /><br />solving the nonlinear system of algebraic equations whose Jacobian matrix is singular<br /><br />at the solution. For this purpose, at first, an auxiliary equation named the homotopy<br /><br />equation is constructed. Then, by differentiating from the homotopy equation, a<br /><br />system of differential equations is replaced instead of the target problem and solved. In<br /><br />other words, the solution of the nonlinear system of algebraic equations with singular<br /><br />Jacobian is transformed to the solution of a system of differential equations. Some<br /><br />numerical tests are presented at the end and the computational efficiency of the<br /><br />method is described.https://ajmc.aut.ac.ir/article_4644_785d5e6be499cc04dc52ada3b7c02cee.pdf