Journal ArticleDOI
A family of high order product integration methods for an integral equation of lighthill
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In this article, a nonlinear singular Volterra integral equation was derived to describe the temperature distribution of the surface of a projectile moving through a laminar boundary layer at high Mach numbers.Abstract:
Lighthill has derived a nonlinear singular Volterra integral equation to describe the temperature distribution of the surface of a projectile moving through a laminar boundary layer at high Mach numbers. This paper presents high order product integration methods for its numerical solution and analyses their convergence. Numerical results are given.read more
Citations
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Numerical solution of a nonlinear Abel type Volterra integral equation
TL;DR: In this article, the analytical and numerical analysis of a nonlinear weakly singular Volterra integral equation is presented, where the smoothness properties of the solution are investigated and it is shown that first order convergence can be achieved away from the origin.
Journal ArticleDOI
Analytical and computational methods for a class of nonlinear singular integral equations
TL;DR: In this article, two product integration methods are proposed and analyzed where the integral over a small initial interval is calculated analytically, allowing the optimal convergence rates to be achieved, under certain conditions, a uniformly convergent iterative solution is obtained on a small interval near the origin.
Computational methods for a nonlinear volterra integral equation
TL;DR: In this article, the numerical solution of a nonlinear weakly singular Volterra integral equation with a nonsmooth solution is considered and the application of product integration methods and a detailed analysis of the Trapezoidal method is given.
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Numerical solution of two-dimensional weakly singular Volterra integral equations with non-smooth solutions
Roghayeh Katani,Sean McKee +1 more
TL;DR: A simple smoothing change of variables is proposed for the solution of two-dimensional nonlinear weakly singular Volterra integral equations of the second kind and a new extension of a discrete Gronwall inequality allows us to prove convergence and obtain an error estimate.
Journal ArticleDOI
Numerical solution of two-dimensional weakly singular Volterra integral equations with non-smooth solutions
TL;DR: In this article , the authors proposed and analyzed a numerical method for the solution of two-dimensional nonlinear weakly singular Volterra integral equations of the second kind, which can have a solution as smooth as is required.
References
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Book
Analysis of Numerical Methods
TL;DR: Reference Record created on 2005-11-18, modified on 2016-08-08 as discussed by the authors, created on 2011-11 -18, created on 2006-11 18 and modified on 2008-08 -08,08
Journal ArticleDOI
Analysis of Numerical Methods. By Isaacson and Keller . Pp. 541 95s. 1966. (Wiley.)
Journal ArticleDOI
Contributions to the Theory of Heat Transfer through a Laminar Boundary Layer
TL;DR: In this article, an approximation to the heat transfer rate across a laminar incompressible boundary layer, for arbitrary distribution of main stream velocity and of wall temperature, is obtained by using the energy equation in von Mises's form, and approximating the coefficients in a manner which is most closely correct near the surface.