On approximate solutions of certain mixed type integrodifferential equations
type: Item
instance of: scholarly article
zbMATH Open document ID: 1265.45015
author: B. G. Pachpatte
publication date: 2012-10-04T00:00:00Z
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45L05
zbMATH DE Number: 6090188
zbMATH Keywords: approximate solutions
zbMATH Keywords: Volterra-Fredholm type
zbMATH Keywords: integrodifferential equations
zbMATH Keywords: integral inequalities
zbMATH Keywords: explicit estimates
MaRDI profile type: Publication
full work available at URL: v10157-011-0025-0
OpenAlex ID: W2077118918
cites work: Collocation Methods for Volterra Integral and Related Functional Differential Equations
cites work: Q5848416
cites work: Q5391253
cites work: Q5425257
cites work: On Fredholm type integral equation in two variables
cites work: Q3632282
DOI: 10.2478/V10157-011-0025-0
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title: On approximate solutions of certain mixed type integrodifferential equations
published in: Analele Științifice ale Universității Al. I. Cuza din Iași. Serie Nouă. Matematică
review text: The paper deals with the initial value problem for the Volterra-Fredholm-type integro-differential equation NEWLINE\[NEWLINEy'(t)=f(t,y(t),(Ay)(t), (By)(t)),\quad t\in [0,a];\quad y(0)=y_0,NEWLINE\]NEWLINE where NEWLINE\[NEWLINE(Ay)(t)=\displaystyle\int_0^tg(t,\sigma,y(\sigma))\,d\sigma,NEWLINE\]NEWLINE NEWLINE\[NEWLINE(By)(t)=\displaystyle\int_0^ah(t,\sigma,y(\sigma))\,d\sigma,NEWLINE\]NEWLINE \(f\in C(I_a\times\mathbb R^3,\mathbb R)\), \(g\in C(D\times\mathbb R,\mathbb R)\), \(h\in C(I_a^2\times\mathbb R,\mathbb R)\), \(I_a=[0,a]\) (\(a>0\)), and \(D=\{(t,s)\in I_a^2: s\leq t\}\). By using some new integral inequalities with explicit estimates, the author studies the \(\varepsilon\)-approximate solutions of the above problem. The corresponding two-dimensional problem is also investigated.
description: scientific article; zbMATH DE number 6090188