Summary

This book has been written for discussing problems in numerical methods and their solutions using Visual C++. The main objective of this book is to provide a bridge between a problem and its solution through visualization. With this in mind, the authors cover the most talked about problems currently available. The first objective is the gap between a problem and its computing elements. A problem normally comes from a practitioner while the computing elements are the work of a programmer. This book provides a bridge to close this gap. The second objective is to disucss a problem, discuss its solution and present the solution in a friendly manner. Today's requirements are very challenging to a problem solver. A numerical solution that plays a series of numbers only will not be appreciated anymore. The solution must be presented in the form of charts, graphs, animation and, sometimes, in the form of multimedia. The interface on the computer should be friendly to the user, where the use of windows, dialogue boxes, mouse, menus and images are necessary. The third objective is to put more emphasis on the problem and try to minimize the coding using MFC. This is necessary since an approach that involves too many codes often distracts the reader from understanding the method for solving the problem

Author Biography

Shaharuddin Salleh, PhD, is Professor in Computational Mathematics, Faculty of Science (Mathematics), Universiti Teknologi, Malaysia (UTM). Dr. Salleh's research is in parallel computing algorithms and scheduling, mobile computing, intelligent systems, and numerical/combinatorial optimization problems. He is also an IT Manager at the Research Management Centre, UTM.

Albert Y. Zomaya, PhD, is the Head of School and CISCO Systems Chair Professor of Internetworking in the School of Information Technologies at the University of Sydney. He is the author or coauthor of several books and more than 300 publications. He is an IEEE Fellow.

Sakhinah Abu Bakar is Lecturer in Computational Mathematics at the School of Mathematical Sciences, Faculty of Science and Technology, National University of Malaysia. She is currently pursuing her PhD degree at the University of Sydney.

Preface	p. xiii
Codes for Download	p. xvii
Modeling and Simulation	p. 1
Numerical Approximation	p. 1
C++ for Numerical Modeling	p. 3
Mathematical Modeling	p. 4
Simulation and Its Visualization	p. 6
Numerical Methods	p. 7
Numerical Applications	p. 7
Fundamental Tools for Mathematical Computing	p. 13
C++ for High-Performance Computing	p. 13
Dynamic Memory Allocation	p. 14
Matrix Reduction Problems	p. 22
Matrix Algebra	p. 35
Algebra of Complex Numbers	p. 43
Number Sorting	p. 51
Summary	p. 54
Programming Challenges	p. 55
Numerical Interface Designs	p. 56
Microsoft Foundation Classes	p. 56
Graphics Device Interface	p. 57
Writing a Basic Windows Program	p. 60
Displaying Text and Graphics	p. 68
Events and Methods	p. 69
Standard Control Resources	p. 71
Menu and File I/O	p. 78
Keyboard Control	p. 87
MFC Compatibility with .Net	p. 92
Summary	p. 95
Curve Visualization	p. 96
Tools for Visualization	p. 96
MyParser	p. 96
Drawing Curves	p. 106
Generating Curves Using MyParser	p. 115
Summary	p. 126
Programming Challenges	p. 126
Systems of Linear Equations	p. 127
Introduction	p. 127
Existence of Solutions	p. 128
Gaussian Elimination Techniques	p. 131
LU Factorization Methods	p. 142
Iterative Techniques	p. 161
Visualizing the Solution: Code5	p. 172
Summary	p. 189
Numerical Exercises	p. 190
Programming Challenges	p. 192
Nonlinear Equations	p. 193
Introduction	p. 193
Existence of Solutions	p. 194
Bisection Method	p. 195
False Position Method	p. 198
Newton-Raphson Method	p. 201
Secant Method	p. 203
Fixed-Point Iteration Method	p. 206
Visual Solution: Code6	p. 208
Summary	p. 225
Numerical Exercises	p. 225
Programming Challenges	p. 226
Interpolation and Approximation	p. 227
Curve Fitting	p. 227
Lagrange Interpolation	p. 228
Newton Interpolations	p. 231
Cubic Spline	p. 239
Least-Squares Approximation	p. 244
Visual Solution: Code7	p. 249
Summary	p. 264
Numerical Exercises	p. 265
Programming Challenges	p. 265
Differentiation and Integration	p. 267
Introduction	p. 267
Numerical Differentiation	p. 268
Numerical Integration	p. 271
Visual Solution: Code8	p. 279
Summary	p. 286
Numerical Exercises	p. 286
Programming Challenges	p. 287
Eigenvalues and Eigenvectors	p. 288
Eigenvalues and Their Significance	p. 288
Exact Solution and Its Existence	p. 289
Power Method	p. 291
Shifted Power Method	p. 292
QR Method	p. 294
Visual Solution: Code9	p. 302
Summary	p. 322
Numerical Exercises	p. 322
Programming Challenges	p. 323
Ordinary Differential Equations	p. 324
Introduction	p. 324
Initial-Value Problem for First-Order ODE	p. 325
Taylor Series Method	p. 327
Runge-Kutta of Order 2 Method	p. 330
Runge-Kutta of Order 4 Method	p. 333
Predictor-Corrector Multistep Method	p. 335
System of First-Order ODEs	p. 338
Second-Order ODE	p. 341
Initial-Value Problem for Second-Order ODE	p. 342
Finite-Difference Method for Second-Order ODE	p. 345
Differentiated Boundary Conditions	p. 351
Visual Solution: Code10	p. 358
Summary	p. 378
Numerical Exercises	p. 378
Programming Challenges	p. 380
Partial Differential Equations	p. 381
Introduction	p. 381
Poisson Equation	p. 385
Laplace Equation	p. 394
Heat Equation	p. 397
Wave Equation	p. 406
Visual Solution: Code11	p. 411
Summary	p. 437
Numerical Exercises	p. 437
Programming Exercises	p. 438
Index	p. 441
Table of Contents provided by Ingram. All Rights Reserved.

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