In this paper, the Taylor polynomial method is used to solve the Helmholtz equation. Using the Taylor polynomial for the method, the Helmholtz equation is transformed into solving matrix equation. The error analysis of this equation is given. A numerical experiment is given to prove the efficiency and dependability of the method.

This paper presents the engineering analytical models of photovoltaic (PV) water pumping system from electronics theory, and some mathematical models of system components have been established. Studies have shown that the minimum unit water cost may not be reached only with the control strategy of maximum output power of the system. Therefore, system optimization is very necessary to reducing the capacity for every unit of pumped water, which is based on the design optimization theory and has shown its economics.