Volterra integral equation

About: Volterra integral equation is a research topic. Over the lifetime, 6228 publications have been published within this topic receiving 114487 citations.

A Technique for the Numerical Solution of Certain Integral Equations of the First Kind

Abstract: where the known functions h(x) , K(x, y) and g(x) are assumed to be bounded and usually to be continuous. If h(x) ~0 the equation is of first kind; if h(x) ~ 0 for a -<_ x ~ b, the equation is of second kind; if h(x) vanishes somewhere but not identically, the equation is of third kind. If the range of integration is infinite or if the kernel K(x, y) is not bounded, the equation is singular. Here we will consider only nonsingular linear integral equations of the first kind:

The Numerical Solution of Integral Equations of the Second Kind

Abstract: Preface 1. A brief discussion of integral equations 2. Degenerate kernel methods 3. Projection methods 4. The Nystrom method 5. Solving multivariable integral equations 6. Iteration methods 7. Boundary integral equations on a smooth planar boundary 8. Boundary integral equations on a piecewise smooth planar boundary 9. Boundary integral equations in three dimensions Discussion of the literature Appendix Bibliography Index.

Differential and Integral Inequalities

Abstract: In 1964 the author's mono graph "Differential- und Integral-Un gleichungen," with the subtitle "und ihre Anwendung bei Abschatzungs und Eindeutigkeitsproblemen" was published The present volume grew out of the response to the demand for an English translation of this book In the meantime the literature on differential and integral in equalities increased greatly We have tried to incorporate new results as far as possible As a matter of fact, the Bibliography has been almost doubled in size The most substantial additions are in the field of existence theory In Chapter I we have included the basic theorems on Volterra integral equations in Banach space (covering the case of ordinary differential equations in Banach space) Corresponding theorems on differential inequalities have been added in Chapter II This was done with a view to the new sections; dealing with the line method, in the chapter on parabolic differential equations Section 35 contains an exposition of this method in connection with estimation and convergence An existence theory for the general nonlinear parabolic equation in one space variable based on the line method is given in Section 36 This theory is considered by the author as one of the most significant recent applications of in equality methods We should mention that an exposition of Krzyzanski's method for solving the Cauchy problem has also been added The numerous requests that the new edition include a chapter on elliptic differential equations have been satisfied to some extent"