Numerical Analysis for Applied Science
Numerical Analysis for Applied Science is a graduate-level text suitable for both scientists and engineers as well as applied mathematicians. Each chapter begins with the motivation and construction of the methods under discussion moves on to practical considerations associated with their implementation, and concludes with an in-depth treatment of rigorous mathematical details. The chapter-end problem sets include both theoretical and computational exercises.
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Some Useful Tools
Approximation of Functions
Direct Methods for Linear Systems
Solution of Nonlinear Equations
Iterative Methods for Linear Systems
Ordinary Differential Equations
Difference Methods for PDEs
Introduction to Finite Elements
algorithm analog apply associated basis functions bounded Chapter coefficients compute condition consider constant COROLLARY cubic defined denote derivatives diagonal entries difference differential discuss eigenvalues eigenvectors Equation error estimate example exists explicit fact Figure finite Fourier Gauss Gauss-Seidel Gauss-Seidel method graph grid function heat equation implies induction initial guess inner product inner-product space integral interval iterative scheme Jacobi method Lemma linear system linearly Lipschitz LU factorization magnitude matrix norm mesh size h Mnxn multiplicity multistep methods multistep scheme Newton-Cotes formulas Newton's method nodes nonsingular nonzero one-step method orthogonal permutation permutation matrix pivoting polynomial interpolation positive definite problem PROOF PROPOSITION prove QR decomposition quadrature requires row reduction satisfies secant method Section sequence solve spline stepsize subinterval successive substitution symmetric and positive theorem tion triangle inequality tridiagonal truncation error upper triangular vanishes vector space yields zero
Applications of Nonstandard Finite Difference Schemes
Ronald E. Mickens
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