Integral equations, Volterra equations, and the remarkable resolvent: contractions

Integral Equations, Volterra Equations, and the Remarkable Resolvent: Contractions

with special accent on the case in which a(t) is unbounded. We use contraction mappings to establish close relations between a(t) and ∫ t 0 R(t, s)a(s)ds. This work gives us a fundamental understanding of the nature of R(t, s). It establishes numerous elementary boundedness results including some from a new point of view. And it tells us that one of our long-held basic assumptions is very incom...

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

Approximate Solution of Linear Volterra-Fredholm Integral Equations and Systems of Volterra-Fredholm Integral Equations Using Taylor Expansion Method

In this study, a new application of Taylor expansion is considered to estimate the solution of Volterra-Fredholm integral equations (VFIEs) and systems of Volterra-Fredholm integral equations (SVFIEs). Our proposed method is based upon utilizing the nth-order Taylor polynomial of unknown function at an arbitrary point and employing integration method to convert VFIEs into a system of linear equ...

Discretization of Volterra Integral Equations

We show that various (discrete) methods for the approximate solution of Volterra (and Abel) integral equations of the first kind correspond to some discrete version of the method of (recursive) collocation in the space of (continuous) piecewise polynomials. In a collocation method no distinction has to be made between equations with regular or weakly singular kernels; the regularity or nonregul...

Oscillation of Volterra Integral Equations and Forced Functional Differential Equations