Volterra Integral and Differential Equations, Volume 202, Second Edition (Mathematics in Science and Engineering)

Most mathematicians, engineers, and many other scientists are well-acquainted with theory and application of ordinary differential equations. This book seeks to present Volterra integral and functional differential equations in that same framework, allowing the readers to parlay their knowledge of ordinary differential equations into theory and application of the more general problems. Thus, the presentation starts slowly with very familiar concepts and shows how these are generalized in a natural way to problems involving a memory.

Concrete Functional Calculus

Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions. This includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear differential equations with the given coefficients. In this book existence and uniqueness of solutions are proved under suitable assumptions for nonlinear integral equations with respect to possibly discontinuous functions having unbounded variation. Key features and topics: Extensive usage of p-variation of functions, and applications to stochastic processes.
 

Introduction to Fortran 95 and Numerical Computing

Contents: a quick tour of fortran 95; the building blocks of a fortran application; flow control; computer arithmetic; applications; intrinsic functions; input and output; arrays; more on procedures; parametrized intrinsic types; derived types; pointers and targets; elements of object-oriented programming; code performance; linear systems of algebraic equations; linear least squares; nonlinear equations; polynomial interpolation; numerical integration; splines; Taylor polynomials

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Numerical Methods for Chemical Engineers with MATLAB Applications

This book emphasizes the derivation of a variety of numerical methods and their application to the solution of engineering problems, with special attention to problems in the chemical engineering field. These algorithms encompass linear and nonlinear algebraic equations, eigenvalue problems, finite difference methods, interpolation, differentiation and integration, ordinary differential equations, boundary-value problems, partial differential equations, and linear and nonlinear regression analysis.

Solution of the Cauchy problem for the Navier - Stokes and Euler equations

Solutions of the Navier-Stokes and Euler equations with initial conditions (Cauchy problem) for two and three dimensions are obtained in the convergence series form by the iterative method using the Fourier and Laplace transforms in this paper. For several combinations of problem parameters numerical results were obtained and presented as graphs.