Perturbed Functional Iterations

A Matrix Free Large-Scale Nonlinear System Solver in Applied Science with an Introduction to D-Mapping
1. Auflage 2024
ISBN: 978-1-032-35029-5
Verlag: Chapman and Hall/CRC

Buch, Englisch, 326 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 658 g

Reihe: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Perturbed functional iterations (PFI) is a large-scale nonlinear system solver. Nature is abundant with events simulated mathematically by nonlinear systems of equations and inequalities. These we call nonlinear models. Often, they are ill-conditioned, meaning small changes in data causing huge changes in the output. PFI, previously called the perturbed iterative scheme (PIS), is a numerical method to solve nonlinear systems of equations in multidimensional space. Computational results demonstrate that this numerical method has some unique features, which have made it more practical for applications in engineering and applied mathematics. This book will guide readers in the proper use of PFI, both in theoretical and practical settings.

Features:

- Ideal resource for postgraduates and professional researchers in science and engineering working in nonlinear systems

- Algorithmically simple enough for engineers and applied scientists to write their own software based on the contents

Zielgruppe

Academic and Postgraduate

Autoren/Hrsg.

Dey, Suhrit

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

Inhaltsverzeichnis

1. Introduction: Why PFI? 2. Numerical Solutions of Equations with One Real Variable. 3. Perturbed Jacobi Iterations. (PFI#1). 4. Perturbation of Gauss-Seidel Iterations. PFI#2 [1]. 5. A More Practical Algorithm of DPFI ( PFI# 3). 6. Initial-Value Problems. 7. Stiff Equations. 8. Boundary Value Problem. 9. Applications to Boundary Layer Flow Models. 10. Numerical Solution of Nonlinear Partial Differential Equations by PFI.

Über Autor(innen)

Suhrit Dey completed his M.A in Applied Mathematics in 1960 from Calcutta University and earned his PhD in Aerospace Engineering at Mississippi State University (MSU). While at MSU, he taught FORTRAN programming in the Department of Computer Science and two upper level graduate courses on Numerical Analysis in the Dept. of Mathematics. In September 1970 he joined the Mathematics Department of Eastern Illinois University (EIU) where he taught a number of courses at the graduate and undergraduate level. During his forty years of tenure at EIU, Prof. Dey published over 70 articles related to computational studies on nonlinear models in applied science and engineering and visited as a visiting professor/ invited colloquium speakers at many universities including London Univ. and Cambridge University, Harvard, Stanford, Yale of USA and in Belgium, Columbia, Germany, France, Italy, Slovenia, Spain, Ireland, Scotland, Poland, Lithuania, Norway, Denmark, Sweden, Finland, and India. He was invited to edit many journals internationally. He received a number of research awards from Illinois Academy of Sc., National Academy of Science of Washington, D.C., Eastern Illinois University, US Dept. of Energy, US Dept. of Defense. Heineman Foundation of Germany, CNR from Italy, Lithuanian Academy of Sc. and Univ. Grant Commission from India and finally from NASA. These awards were mostly for his works on PFI (Perturbed Functional Iteration) which he developed to solve nonlinear systems of equations numerically with applications to Fluid Dynamics, Environmental Science, Biophysics, Chemical Kinetics, and many other different areas in Engineering.