Asymptotic solution to convolution integral equations on large and small intervals

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 ...

On the Numerical Solution of Convolution Integral Equations and Systems of such Equations

Convolution spline approximations of Volterra integral equations

We derive a new “convolution spline” approximation method for convolution Volterra integral equations. This shares some properties of convolution quadrature, but instead of being based on an underlying ODE solver is explicitly constructed in terms of basis functions which have compact support. At time step tn = nh > 0, the solution is approximated in a “backward time” manner in terms of basis f...

Numerical solution of Fredholm integral-differential equations on unbounded domain

In this study, a new and efficient approach is presented for numerical solution of Fredholm integro-differential equations (FIDEs) of the second kind on unbounded domain with degenerate kernel based on operational matrices with respect to generalized Laguerre polynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultili...

Integral equations, large and small forcing functions: Periodicity

The defining property of an integral equation with resolvent R(t, s) is the relation between a(t) and ∫ t 0 R(t, s)a(s)ds for functions a(t) in a given vector space. We study the behavior of a solution of an integral equation x(t) = a1(t) + a2(t) − ∫ t 0 C(t, s)x(s)ds when a1(t) is periodic, C(t+ T, s+ T ) = C(t, s), while a2(t) is typified by (t+ 1) β with 0 < β < 1. There is a resolvent, R(t,...