Numeric Computing in Fortran - Hardcover

Bose, Sujit Kumar

Hardcover

ISBN 10: 1842654772 ISBN 13: 9781842654774

Publisher: Alpha Science, 2009

Synopsis

Scientific enquiry mostly require computation of mathematical models. Numeric Computing in Fortran endeavours to systematically develop the principal methods of solution of such problems, develop the algorithms in an organized manner and provides understandable computer codes in simple statements of Fortran 90/95 a traditional language for such purposes. This forward looking version of the language is fully backward-compatible to facilitate integration with user written programs. The mathematics behind the computational methods is kept at a moderate level and proofs of the theoretical results are provided in most cases.

Table of Contents

• Preface
• Computation in Fortran: Calculators and Computers
• Errors in Computing
• Complexity of Algorithms
• Elements of FORTRAN
• Equations: Real Roots
• The General Iteration Method
• Rate of Convergence
• Convergence Theorems
• Complex Roots
• Algebraic Equations
• Choice of Method
• System of Equations: Linear System of Equations
• Error: Matrix Norms and Condition Number
• Relaxation Methods
• Nonlinear System of Equations
• Interpolation: Polynomial Interpolation
• Equally Spaced Points: Finite Differences
• Best Interpolation Nodes: Chebyshev Interpolation
• Piecewise Polynomial Spline Interpolation
• Differentiation and Integration: Numerical Differentiation
• Numerical Integration
• Euler-Maclaurin Summation Formula
• Improper Integrals
• Double Integration
• Ordinary Differential Equations: Initial Value Problem for First Order ODE
• System of ODEs
• Stiff Differential Equations
• Boundary Value Problems
• Partial Differential Equations: First Order Equation
• The Diffusion Equation
• The Wave Equation
• Poisson Equation
• Diffusion and Wave Equations in Two Dimension
• Convergence: Lax's Equivalence Theorem
• Approximation: Uniform Approximation by Polynomials
• Best Uniform (Minimax) Approximation
• Least Squares Approximation
• Orthogonal Polynomials
• Orthogonal Polynomials Over Discrete Set of Points: Smoothing of Data
• Trigonometric Approximation
• Rational Approximations
• Matrix Eigenvalues: General Theorems
• Real Symmetric Matrices
• General Matrices
• Maximum Modulus Eigenvalue: The Power Method
• The Characteristic Equation
• Fast Fourier Transform: Discrete Fourier Transform
• Fast Fourier Transform
• FFT for N = r1r2rm
• Bibliography
• Index.

About this title

About the Author

Sujit Kumar Bose.: S. N. Bose National Centre for Basic Sciences Kolkata

Edition details

• Publisher: Alpha Science
• Publication date: 2009
• Language: English
• ISBN 10: 1842654772
• ISBN 13: 9781842654774
• Binding: Hardcover
• Number of pages: 432