A new method for the numerical solution of simultaneous nonlinear equations

摘要

A new technique is developed for the numerical solution of simultaneous nonlinear equations (SNEs). This is achieved by the iterative solution of a parametric linear system coupled with a nonlinear single variable equation. The new technique converges very quickly, and is ideal for cases where the system of equations can be easily differentiated. It is motivated by the multivariable Newton–Raphson (mNR) method and is approximately of second-order convergence. Furthermore, we introduce the “zeros Jacobian” for the Jacobian evaluated at some arbitrary zeros of the vector function components. This is utilized in computing a feasible starting point for SNEs. The computation of a starting point would be very useful for systems where one has no prior knowledge of the possible solutions.