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New algorithm for the numerical solution of the integro-differential equation with an integral boundary condition. (English) Zbl 1187.92094
Summary: In this paper, a sequence of approximate solutions converging uniformly to the exact solution for a class of integro-differential equations with an integral boundary condition arising in chemical engineering, underground water flow and population dynamics and other fields of physics and mathematical chemistry are obtained by using an iterative method. An exact solution is represented in the form of series in the reproducing kernel space. The $n$-term approximation ${u}_{n}\left(x\right)$ is proved to converge to the exact solution $u\left(x\right)$. Moreover, the first derivative of ${u}_{n}\left(x\right)$ is also convergent to the first derivative of $u\left(x\right)$.
##### MSC:
 92E99 Applications of mathematics to chemistry 65R99 Numerical methods for integral equations and transforms 92F05 Applications of mathematics to other natural sciences
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