E-ISBN: Publication Year: 2009
Binding: Paper Back Dimension: 185mm x 240mm Weight: 700
About the book
Scientific enquiry mostly require computation of mathematical models. Numeric Computing in Fortran endeavors 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.
The book will be useful for traditional courses of Numerical Methods/ Analysis in Engineering, Natural Sciences and Mathematics. It will be a useful text for researchers in these subjects and for those who prefer to write their own programs.
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 = r1r2…rm / Bibliography / Index.