Fractional Differential Equations

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

EDDINGTON'S “Internal Constitution of the Stars” was published in 1926 and gives what now ranks as a classical account of his own researches and of the general state of the theory at that time. Since then, a tremendous amount of work has appeared. Much of it has to do with the construction of stellar models with different equations of state applying in different zones. Other parts deal with the effects of varying chemical composition, with pulsation and tidal and rotational distortion of stars, and with the precise relations between the interior and the atmosphere of a star. The striking feature of all this work is that so much can be done without assuming any particular mechanism of stellar energy-generation. Only such very comprehensive assumptions are made about the distribution and behaviour of the energy sources that we may expect future knowledge of their mechanism to lead mainly to more detailed results within the framework of the existing general theory. An Introduction to the Study of Stellar Structure By S. Chandrasekhar. (Astrophysical Monographs sponsored by The Astrophysical Journal.) Pp. ix+509. (Chicago: University of Chicago Press; London: Cambridge University Press, 1939.) 50s. net.

An Introduction to the Study of Stellar Structure

高等学校計算数学学報 = Numerical mathematics

Boundary Value Problems in Physics and Engineering By Frank Chorlton. Pp. 250. (Van Nostrand: London, July 1969.) 70s

Boundary value problems

The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials

In this study, a matrix method called the Taylor collocation method is presented for numerically solving the linear integro-differential equations by a truncated Taylor series. Using the Taylor collocation points, this method transforms the integro-differential equation to a matrix equation which corresponds to a system of linear algebraic equations with unknown Taylor coefficients. Also the method can be used for linear differential and integral equations. To illustrate the method, it is applied to certain linear differential, integral, and integro-differential equations and the results are compared.

A Taylor Collocation Method for the Solution of Linear Integro-Differential Equations

The method of Kanwal and Liu for the solution of Fredholm integral equations is applied to certain linear and nonlinear Volterra integral equations of the second kind. Some equations considered by other authors are solved in terms of Taylor polynomials and the results are compared.

Taylor polynomial solutions of Volterra integral equations

A matrix method is introduced for the approximate solution of the second‐order linear differential equation with specified associated conditions in terms of Taylor polynomials about any point. Examples are presented which illustrate the pertinent features of the method. Also it is applied to the generalized Hermite, Laguerre, Legendre and Chebyshev equations given by Costa and Levine.

Mehmet Sezer

Papers

The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials

A Taylor Collocation Method for the Solution of Linear Integro-Differential Equations

Taylor polynomial solutions of Volterra integral equations

A method for the approximate solution of the second‐order linear differential equations in terms of Taylor polynomials

Approximate solution of multi-pantograph equation with variable coefficients