Numerical Analysis: Mathematics of Scientific Computing

  title={Numerical Analysis: Mathematics of Scientific Computing},
  author={David R. Kincaid and Ward Cheney},
This work treats numerical analysis from a mathematical point of view, demonstrating that the many computational algorithms and intriguing questions of computer science arise from theorems and proofs. Algorithms are developed in pseudocode, with the intention of making it easy for students to write computer routines in a number of standard programming languages, including BASIC, Fortran, C and Pascal. 
Numerical continuation in classical mechanics and thermodynamics
In this paper, modern numerical continuation methodologies are presented as a way of understanding and computing multiplicity of solutions in undergraduate physics problems. Mechanical and
A note on a family of quadrature formulas and some applications
In this paper a construction of a one-parameter family of quadrature formulas is presented. This family contains the classical quadrature formulas: trapezoidal rule, midpoint rule and two-point Gauss
of Mathematics And its Applications OpenType Quadrature Methods with Equispaced Nodes and a Maximal Polynomial Degree of Exactness Research
In this paper we develop Open-Type Quadrature Method. If the interval of definite integral can divided a number of equal subinterval then We are using the nodes of Quadrature Method as mid-point of
Solving a nonlinear equation by a uniparametric family of iterative processes
A convergence analysis for a real function depending of one real parameter α ∊  and it is proved that the authors can always apply a method of this family to solve f(x) = 0.
Algorithms and Complexity for some Multivariate Problems
This work studies multivariate problems like function approximation, numerical integration, global optimization and dispersion, and presents optimal algorithms for some of these problems on the information complexity $n(\varepsilon,d)$ ofThese problems.
Graphic and numerical comparison between iterative methods
generates a sequence {xn}n=0 that converges to ζ. In fact, Newton’s original ideas on the subject, around 1669, were considerably more complicated. A systematic study and a simplified version of the
Iterative numerical methods for nonlinear systems
Some valuable techniques in mathematical modeling are presented by outlining basic, iterative numerical methods for solving nonlinear systems of equations.
Solution for Partial Differential Equations Involving Logarithmic Nonlinearities
In this paper, a modification of He's variational iteration method by using r terms of Taylor's series is applied for finding the solution of Kolmogorov-Petrovskii-Piskunov and Klein- Gordon