A FOURTH-ORDER MODIFIED ITERATIVE SOLVER FOR SOLVING NONLINEAR EQUATIONS

Abstract

Effective and precise numerical techniques are crucial for identifying the roots of nonlinear equations, which commonly appear in engineering, applied mathematics, physics, and scientific computing. Nonlinear equations are frequently solved using classical techniques like the Newton-Raphson Method (NR) and the Regula-Falsi Method (RF); however, the computational effectiveness of these techniques depends on the problem's features and the initial approximations. In order to increase convergence efficiency, a Modified Iterative Solver (MIS) is suggested in this paper as an adaptation of the Newton–Raphson method. Four benchmark nonlinear equations containing exponential, trigonometric, and polynomial functions are used to assess the suggested approach, which is implemented in Wolfram Mathematica. In terms of iteration count, residual error, and Experimental Order of Convergence (EOC), its numerical performance is compared with that of RF and NR. According to the given numerical results, MIS converges in two iterations for the chosen test problems, while NR takes three to four iterations and RF takes eight to eighty-seven. For each of the four test problems, the EOC analysis produces values almost equal to four, offering numerical proof of fourth-order convergence under the examined circumstances. These results suggest that the suggested approach holds promise for effectively resolving the benchmark nonlinear equations taken into consideration in this investigation. Its wider applicability and convergence features would be established by more research employing more test cases and theoretical convergence analysis.