Computing for Numerical Methods Using Visual C++

Computing for Numerical Methods Using Visual C++ 
Shaharuddin Salleh, Albert Y. Zomaya, Sakhinah A. Bakar 
ISBN: 978-0-470-12795-7
Hardcover
448 pages
January 2008

Computing for Numerical Methods Using Visual C++ fills the need for a complete, authoritative book on the visual solutions to problems in numerical methods using C++. The book takes an interdisciplinary approach to the subject and demonstrates how solving problems in numerical methods using C++ is dominant and practical for implementation due to its flexible language format, object-oriented methodology, and support for high numerical precisions.

Chapter 1: Overview of C++. 
Language style and organization. 
Data types, variables. 
Loops and branches. 
Array, pointer, function, structure. 
Classes and objects. 
Inheritance, polymorphism, encapsulation. 
Complexity analysis. 

Chapter 2: Visual C++ Methods. 
MFC library . 
Fundamental interface tools. 
Text displays. 
Graphics and images. 
Writing the first program. 

Chapter 3: Fundamental Mathematical Tools. 
C++ for High-Performance Computing. 
Dynamic memory allocation. 
Allocation for one-dimensional arrays. 
Allocation for higher-dimensional arrays. 
Case Study: Matrix multiplication problem. 
Matrix elimination problems. 
Vector and matrix norms. 
Row operations. 
Matrix reduction to triangular form. 
Computing the determinant of a matrix. 
Computing the inverse of a matrix. 
Matrix algebra. 
Data passing between functions. 
Matrix addition and subtraction. 
Matrix multiplication. 
Matrix inverse. 
Putting the pieces together. 
Algebra of complex numbers. 
Addition and subtraction. 
Multiplication. 
Conjugate. 
Division. 
Inverse of a complex number. 
Putting the pieces together. 
Number Sorting. 
Programming Exercises. 

Chapter 4: System of Linear Equations. 
Systems of Linear Systems. 
Existence of Solutions. 
Elimination Techniques. 
Gauss Elimination Method. 
Gauss Elimination with Partial Pivoting. 
Gauss-Jordan Method. 
LU Factorization Techniques. 
Crout Method. 
Doolittle Method. 
Cholesky Method. 
Thomas Algorithm. 
Iterative Techniques. 
Jacobi Method. 
Gauss-Seidel Method. 
Visual C++ Solution Interface. 
Summary. 
Programming Exercises. 

Chapter 5: Nonlinear Equations. 
Iterative methods: convergence, stability. 
Background: existence of solution, MVT, errors, etc.. 
Bisection method. 
False-point position method. 
Newton method. 
Secant method. 
Fixed-point iterative method. 
Visual C++ Solution Interface. 
Summary. 
Programming Exercises. 

Chapter 6: Interpolation and Approximation. 
Concepts, existence, stability. 
Lagrange. 
Newton methods: forward, backward. 
Stirling method. 
Cubic spline interpolation. 
Least-square approximation. 
Visual C++ Solution Interface. 
Summary. 
Programming Exercises. 

Chapter 7: Differentiation and Integration. 
Taylor series. 
Newton methods (forward, backward, central). 
Trapezium method. 
Simpson method. 
Simpson 3/8 method. 
Gauss quadrature. 
Visual C++ Solution Interface. 
Summary. 
Programming Exercises. 

Chapter 8: Eigenvalues and Eigenvectors. 
Characteristic polynomials. 
Power method. 
Power method with shifting. 
Visual C++ Solution Interface. 
Summary. 
Programming Exercises. 

Chapter 9: Ordinary Differential Equations. 
Existence, uniqueness, stability, convergence. 
IVP: Taylor method. 
Euler method. 
Runge-Kutta of order 2 method. 
Runge-Kutta of order 4 method. 
Higher dimensional orders. 
Multistep methods: Adams-Bashforth method. 
Boundary Value Problems: finite-difference method. 
Visual C++ Solution Interface. 
Summary. 
Programming Exercises. 

Chapter 10: Partial Differential Equations. 
Existence, uniqueness, stability, convergence. 
Elliptic problem: Laplace equation. 
Elliptic problem: Poisson equation. 
Parabolic problem: heat equation. 
Hyperbolic problem: wave equation. 
Visual C++ Solution Interface. 
Summary. 
Programming Exercises. 

Chapter 11: Finite Element Methods. 
One-dimensional heat problem. 
Linear approximation. 
Quadratic approximation. 
Two-dimensional problem: triangulation method.
Visual C++ Solution Interface. 
Summary. 
Programming Exercises

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