Fundamentals of engineering numerical analysis
Parviz Moin
- 2nd Ed.
- Cambridge, UK ; New York : Cambridge University Press, 2001.
- xiv, 209 pages : illustrations ; 26 cm
Interpolation -- Lagrange Polynomial Interpolation -- Cubic Spline Interpolation -- Numerical Differentiation--Finite Differences -- Construction of Difference Formulas Using Taylor Series -- A General Technique for Construction of Finite Difference Schemes -- An Alternative Measure for the Accuracy of Finite Differences -- Pade Approximations -- Non-Uniform Grids -- Numerical Integration -- Trapezoidal and Simpson's Rules -- Error Analysis -- Trapezoidal Rule with End-Correction -- Romberg Integration and Richardson Extrapolation -- Adaptive Quadrature -- Gauss Quadrature -- Numerical Solution of Ordinary Differential Equations -- Initial Value Problems -- Numerical Stability -- Stability Analysis for the Euler Method -- Implicit or Backward Euler -- Numerical Accuracy Revisited -- Trapezoidal Method -- Linearization for Implicit Methods -- Runge--Kutta Methods -- Multi-Step Methods -- System of First-Order Ordinary Differential Equations -- Boundary Value Problems -- Shooting Method -- Direct Methods -- Numerical Solution of Partial Differential Equations -- Semi-Discretization -- von Neumann Stability Analysis -- Modified Wavenumber Analysis -- Implicit Time Advancement -- Accuracy via Modified Equation -- Du Fort--Frankel Method: An Inconsistent Scheme -- Multi-Dimensions -- Implicit Methods in Higher Dimensions -- Approximate Factorization -- Stability of the Factored Scheme -- Alternating Direction Implicit Methods -- Mixed and Fractional Step Methods -- Elliptic Partial Differential Equations.
Introduction to numerical techniques useful in solving complex engineering problems.