**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

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