TY - JOUR
ID - 4644
TI - Numerical differential continuation approach for systems of nonlinear equations with singular Jacobian
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN - 2783-2449
AU - Mehrpouya, Mohammad Ali
AD - Department of Mathematics, Tafresh University, 39518-79611, Tafresh, Iran
Y1 - 2022
PY - 2022
VL - 3
IS - 1
SP - 53
EP - 58
KW - Nonlinear equations
KW - Newton’s method
KW - Singular Jacobian
KW - Continuation method
DO - 10.22060/ajmc.2021.20487.1068
N2 - 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.
UR - https://ajmc.aut.ac.ir/article_4644.html
L1 - https://ajmc.aut.ac.ir/article_4644_e756b9224e879823a1de07090b1f42f9.pdf
ER -