FINITE VOLUME AND WEIGHTED RESIDUALS METHODS FOR SOLVING MAXWELL’ S EQUATIONS | طريقة الحجم المحدود وطريقة القيم المتبقية لحل معادلات ماكسويل

The Finite Volume Method (FVM) and the Method of Weighted Residuals (MWR), two numerical techniques for solving Maxwell's equations—which characterize electromagnetic fields—are compared in this work. Numerous technological fields, including electrical engineering, wireless communication, and electromagnetic wave patterns, depend on Maxwell's equations. The Finite Volume Method ensures that the flow of quantities (fluxes) is preserved at the boundaries by dividing the problem region into small volumes and applying conservation principles to each one of them separately. This method is frequently implemented in fluid dynamics and electromagnetic simulations and is particularly of use for problems demanding exact flux conservation. The Method of Weighted Residuals uses specific weighting functions to reduce the errors (residuals) in the governing equations after making a precise assumption of an approximate solution. If the appropriate pilot functions are used, this approach can be highly precise and is adaptable, making it appropriate for complex forms and boundary conditions. This work scrutinizes the two approaches MATLAB implementations and evaluates how well they solve Maxwell's equations. Precision, computational efficacy, and convenience are the main comparing points. The findings demonstrate that MWR provides greater resilience and can be more precise in complex scenarios, even though FVM is more accurate at saving flux in particular. All things taken into account, this work contributes to the progress of effective numerical techniques in problem solving strategies, which may be of exceptional advantage in future cutting-edge technologies.