Numerical Methods for Fractional Calculus

ISBN-13: 9781482253801 / Angielski / Twarda / 2015 / 300 str.

Changpin Li; Fanhai Zeng

Opis

Numerical Methods for Fractional Calculus presents numerical methods for fractional integrals and fractional derivatives, finite difference methods for fractional ordinary differential equations (FODEs) and fractional partial differential equations (FPDEs), and finite element methods for FPDEs. The book introduces the basic definitions and properties of fractional integrals and derivatives before covering numerical methods for fractional integrals and derivatives. It then discusses finite difference methods for both FODEs and FPDEs, including the Euler and linear multistep methods. The final chapter shows how to solve FPDEs by using the finite element method. This book provides efficient and reliable numerical methods for solving fractional calculus problems. It offers a primer for readers to further develop cutting-edge research in numerical fractional calculus. MATLAB^(r) functions are available on the book s CRC Press web page."

Recenzje

"The book provides a survey of many different methods for the numerical computation of Riemann–Liouville integrals of fractional order and of fractional derivatives of Riemann–Liouville, Caputo, and Weyl type. Algorithms for the solution of associated ordinary differential equations and certain special classes of partial differential equations are presented as well."
—Zentralblatt MATH 1326

Spis treści

Introduction to Fractional Calculus. Numerical Methods for Fractional Integral and Derivatives. Numerical Methods for Fractional Ordinary Differential Equations. Finite Difference Methods for Fractional Partial Differential Equations. Galerkin Finite Element Methods for Fractional Partial Differential Equations. Bibliography. Index.