Fundamental Numerical Methods for Electrical Engineering

Front Cover
Springer Science & Business Media, Jul 17, 2008 - Technology & Engineering - 284 pages
0 Reviews
Stormy development of electronic computation techniques (computer systems and software), observed during the last decades, has made possible automation of data processing in many important human activity areas, such as science, technology, economics and labor organization. In a broadly understood technology area, this developmentledtoseparationofspecializedformsofusingcomputersforthedesign and manufacturing processes, that is: – computer-aided design (CAD) – computer-aided manufacture (CAM) In order to show the role of computer in the rst of the two applications m- tioned above, let us consider basic stages of the design process for a standard piece of electronic system, or equipment: – formulation of requirements concerning user properties (characteristics, para- ters) of the designed equipment, – elaboration of the initial, possibly general electric structure, – determination of mathematical model of the system on the basis of the adopted electric structure, – determination of basic responses (frequency- or time-domain) of the system, on the base of previously established mathematical model, – repeated modi cation of the adopted diagram (changing its structure or element values) in case, when it does not satisfy the adopted requirements, – preparation of design and technological documentation, – manufacturing of model (prototype) series, according to the prepared docum- tation, – testing the prototype under the aspect of its electric properties, mechanical du- bility and sensitivity to environment conditions, – modi cation of prototype documentation, if necessary, and handing over the documentation to series production. The most important stages of the process under discussion are illustrated in Fig. I. 1. xi xii Introduction Fig. I.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Selected pages

Contents

Methods for Numerical Solution of Linear Equations
1
112 The GaussJordan Elimination Method
9
113 The LU Matrix Decomposition Method
11
114 The Method of Inverse Matrix
14
12 Indirect or Iterative Methods
17
122 Jacobi and GaussSeidel Methods
18
13 Examples of Applications in Electrical Engineering
23
References
27
532 The Simpson Cubature Formula
148
54 An Example of Applications
151
References
154
Numerical Differentiation of One and Two Variable Functions
155
61 Approximating the Derivatives of One Variable Functions
157
62 Calculating the Derivatives of One Variable Function by Differentiation of the Corresponding Interpolating Polynomial
163
63 Formulas for Numerical Differentiation of Two Variable Functions
168
64 An Example of the TwoDimensional Optimization Problem and its Solution by Using the Gradient Minimization Technique
172

Methods for Numerical Solving the Single Nonlinear Equations
29
21 Determination of the Complex Roots of Polynomial Equations by Using the Lins and Bairstows Methods
30
212 Bairstows Method
32
213 Laguerre Method
35
22 Iterative Methods Used for Solving Transcendental Equations
36
221 Bisection Method of Bolzano
37
222 The Secant Method
38
223 Method of Tangents NewtonRaphson
40
23 Optimization Methods
42
24 Examples of Applications
44
References
47
Methods for Numerical Solution of Nonlinear Equations
49
32 The Iterative Parameter Perturbation Procedure
51
33 The Newton Iterative Method
52
34 The Equivalent Optimization Strategies
56
35 Examples of Applications in the Microwave Technique
58
References
68
Methods for the Interpolation and Approximation of One Variable Function
69
41 Fundamental Interpolation Methods
72
412 The Lagrange Interpolating Polynomial
73
413 The Aitken Interpolation Method
76
414 The NewtonGregory Interpolating Polynomial
77
415 Interpolation by Cubic Spline Functions
82
416 Interpolation by a Linear Combination of Chebyshev Polynomials of the First Kind
86
42 Fundamental Approximation Methods for One Variable Functions
89
422 The Maximally Flat Butterworth Approximation
94
423 Approximation Curve Fitting by the Method of Least Squares
97
424 Approximation of Periodical Functions by Fourier Series
102
43 Examples of the Application of Chebyshev Polynomials in Synthesis of Radiation Patterns of the InPhase Linear Array Antenna
111
References
120
Methods for Numerical Integration of One and Two Variable Functions
121
51 Integration of Definite Integrals by Expanding the Integrand Function in Finite Series of Analytically Integrable Functions
123
52 Fundamental Methods for Numerical Integration of One Variable Functions
125
522 The Romberg Integration Rule
130
523 The Simpson Method of Integration
132
524 The NewtonCotes Method of Integration
136
525 The Cubic Spline Function Quadrature
138
526 The Gauss and Chebyshev Quadratures
140
53 Methods for Numerical Integration of Two Variable Functions
147
References
177
Methods for Numerical Integration of Ordinary Differential Equations
178
72 The OneStep Methods
180
722 The Heun Method
182
723 The RungeKutta Method RK 4
184
724 The RungeKuttaFehlberg Method RKF 45
186
73 The Multistep PredictorCorrector Methods
189
731 The AdamsBashforthMoulthon Method
193
732 The MilneSimpson Method
194
733 The Hamming Method
197
74 Examples of Using the RK 4 Method for Integration of Differential Equations Formulated for Some Electrical Rectifier Devices
199
742 The FullWave Rectifier Integrated with the ThreeElement LowPass Filter
204
743 The Quadruple Symmetrical Voltage Multiplier
208
75 An Example of Solution of Riccati Equation Formulated for a Nonhomogenous Transmission Line Segment
215
76 An Example of Application of the Finite Difference Method for Solving the Linear Boundary Value Problem
219
References
221
The Finite Difference Method Adopted for Solving Laplace Boundary Value Problems
223
81 The Interior and External Laplace Boundary Value Problems
226
82 The Algorithm for Numerical Solving of TwoDimensional Laplace Boundary Problems by Using the Finite Difference Method
228
821 The Liebmann Computational Procedure
231
822 The Successive OverRelaxation Method SOR
238
83 Difference Formulas for Numerical Calculation of a Normal Component of an Electric Field Vector at Good Conducting Planes
242
Impedance and Attenuation Coefficient for Some TEM Transmission Lines
245
841 The Shielded Triplate Stripline
246
842 The Square Coaxial Line
249
843 The Triplate Stripline
251
844 The Shielded Inverted Microstrip Line
253
845 The Shielded Slab Line
258
846 Shielded Edge Coupled Triplate Striplines
263
References
268
Equation of a Plane in ThreeDimensional Space
269
The Inverse of the Given Nonsingular Square Matrix
271
The Fast Elimination Method
273
The Doolittle Formulas Making Possible Presentation of a Nonsingular Square Matrix in the form of the Product of Two Triangular Matrices
275
Difference Formula for Calculation of the Electric Potential at Points Lying on the Border Between two Looseless Dielectric Media Without Electrical...
277
Complete Elliptic Integrals of the First Kind
279
Subject Index
281
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information