Newton-like Schemes via the Method of Generalized Quasilinearization for Volterra Integral Equations of the Second Kind

Cesar Martinez-Garza


In this paper we use the Method of Generalized Quasilinearization to obtain Newton-like comparative schemes to solve the Volterra Integral equation of the Second Kind: $0=f(t,x)+\int_{t_0}^t K(t,s,x(s))ds$, which has an isolated zero, $x(t)=r(t)$ in ~$\Omega$ with  ~$\Omega=\{(x,t)|\a_0(t)\leq x\leq\b_0(t),t\in J\}$, $J=[t_0,t_0 +T],~ T>0$,~where $f(t,x) \in C^{0,2}[J \times \Omega,\mathbb{R}]$, $K(t,s,x) \in C^{0,2}[J\times J\times\Omega,\mathbb{R}]$. Several cases where $f$ and $K$ are convex or concave functions are presented.

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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