Efficient method for solving a system of nonlinear equations

Various problems of pure and applied sciences can be studied in the unified frame work of the system of nonlinear equations. By using decomposition technique in conjunction with the coupled system of equations, we develop new iterative method for solving a system of nonlinear equations, which has better efficiency index. We prove the fifth-order convergence of the proposed method. We provide the comparison of efficiency index with some other well-known methods. For the implementation and performance of the new method, we solve the kinematic synthesis problem for steering, Chandrasekhar integral equation and combustion problem for a temperature of 3000 °C and compare the results with some existing methods.