Numerical differential continuation approach for systems of nonlinear equations with singular Jacobian | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 7، دوره 3، شماره 1، اردیبهشت 2022، صفحه 53-58 اصل مقاله (321.16 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2021.20487.1068 | ||
| نویسنده | ||
| Mohammad Ali Mehrpouya* | ||
| Department of Mathematics, Tafresh University, 39518-79611, Tafresh, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Nonlinear equations؛ Newton’s method؛ Singular Jacobian؛ Continuation method | ||
| مراجع | ||
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