Page 15 - Excel for Scientists and Engineers: Numerical Methods

xii EXCEL: NUMERICAL METHODS

The Gauss-Seidel Method Implemented on a Worksheet ............................ 203
The Gauss-Seidel Method Implemented on a Worksheet
Using Circular References ........................................................................ 204
A Custom Function Procedure for the Gauss-Seidel Method ...................... 205
Solving Nonlinear Systems by Iteration ............................................................. 207
Newton's Iteration Method .......................................................................... 207
Problems ............................................................................................................. 213
Chapter 10 Numerical Integration of Ordinary Differential Equations
Part I: Initial Conditions 217
Solving a Single First-Order Differential Equation ............................................ 218
Euler's Method ............................................................................................. 218
The Fourth-Order Runge-Kutta Method ..................................................... 220
Fourth-Order Runge-Kutta Method Implemented on a Worksheet ............. 220
Runge-Kutta Method Applied to a Differential Equation
Involving Both x and y ............................................................................. 223
Fourth-Order Runge-Kutta Custom Function
for a Single Differential Equation with the Derivative Expression
Coded in the Procedure ............................................................................ 224
Fourth-Order Runge-Kutta Custom Function
for a Single Differential Equation with the Derivative Expression
Passed as an Argument ............................................................................. 225
Systems of First-Order Differential Equations ................................................... 228
Fourth-Order Runge-Kutta Custom Function
for Systems of Differential Equations ...................................................... 229
Predictor-Corrector Methods., ............................................................................ 235
A Simple Predictor-Corrector Method ......................................................... 235
A Simple Predictor-Corrector Method
Utilizing an Intentional Circular Reference .............................................. 236
Higher-Order Differential Equations ................................................................. 238
Problems ............................................................................................................. 241

Chapter 11 Numerical Integration of Ordinary Differential Equations
Part II: Boundary Conditions 245
The Shooting Method ......................................................................................... 245
An Example: Deflection ofa Simply Supported Beam ............................... 246
Solving a Second-Order Ordinary Differential Equation
by the Shooting Method and Euler's Method ........................................... 249
Solving a Second-Order Ordinary Differential Equation
by the Shooting Method and the RK Method ........................................... 251
Finite-Difference Methods ................................................................................. 254
Solving a Second-Order Ordinary Differential Equation
by the Finite-Difference Method .............................................................. 254