... Generating Blend Surfaces Using Partial DifferentialEquations Computer-Aided Design 1989, 21:165-171 Ugail H, Bloor MIG, Wilson MJ: Techniques for Interactive Design Using the PDE Method ACM ... a closed form analytic solution of Equations (1) and (2) Choosing the parametric region to be ≤ u ≤ and ≤ v ≤ 2π, and assuming that the conditions given in Equations (3), (4) and (5) are periodic ... specific forms of A0 (u), An (u), Bn (u) and R(u, v) for the case of Equations (1) can be found in [17] and for the case of Equations (2) can be found in [21] The main point to bear in mind regarding...
... CHAPTER ONE MATLAB FUNDAMENTALS MATLAB is a numeric computation software for engineering and scientific calculations The name MATLAB stands for MATRIX LABORATORY MATLAB is primarily a ... accuracy MATLAB has a rich set of plotting capabilities The graphics are integrated in MATLAB Since MATLAB is also a programming environment, a user can extend the functional capabilities of MATLAB ... specific domain 1.1 MATLAB BASIC OPERATIONS When MATLAB is invoked, the command window will display the prompt >> MATLAB is then ready for entering data or executing commands To quit MATLAB, type the...
... MathWorks, Inc., MATLAB, High-Performance Numeric Computation Software, 1995 Biran, A and Breiner, M., MATLAB for Engineers, AddisonWesley, 1995 Etter, D.M., Engineering Problem Solving with MATLAB, 2nd ... ≥ 3.5 Write a MATLAB program to convert analog signal x to digital signal y Test the program by using an analog signal with the following amplitudes: -1.25, 2.57 and 6.0 Solution MATLAB Script ... Consider the following MATLAB statements: x = input(‘Enter age of student’); if x < error(‘wrong age was entered, try again’) end x = input(‘Enter age of student’) For the above MATLAB statements,...
... derivatives at the point A are evaluated using the points to which A is shown connected The second derivatives at point B are evaluated using the connected points and also using “right-hand side” boundary ... effectiveness of the conjugate gradient algorithm for solving finite-difference equations However, it is useful when incorporated in methods that first rewrite the equations so that A is transformed to a matrix ... boundary value problem are: • What are the variables? • What equations are satisfied in the interior of the region of interest? • What equations are satisfied by points on the boundary of the region...
... useful for solving RLC circuit problems From the RLC circuit, we write differentialequations by using network analysis tools The differentialequations are converted into algebraic equationsusing ... i1 (5.40) MATLAB functions for solving ordinary differentialequations are ODE functions These are described in the following section 5.4.1 MATLAB Ode Functions MATLAB has two functions, ... containing the above differentialequationsMATLAB Script % % solution of a set of first order differentialequations % the function diff3(t,v) is created to evaluate % the differential equation...
... can be used to write equations for each mesh that does not contain a dependent or independent current source Using KVL and writing equations for each mesh, the resulting equations will have the ... (4.36) Using KVL for loop 1, we have − 10 I a + Vb + 5I a + 8( I a + 5) = (4.37) UsingEquations (4.31) and (4.32), Equation (4.37) becomes − 10 I a + Vb + 5I a + I a + 40 = i.e., 3I a + Vb = −40 Using ... current from a set of simultaneous equations The latter equations are easily set up if the circuit can be drawn in planar fashion This implies that a set of simultaneous equations can be obtained if...
... implicit schemes, which require us to solve implicit equations coupling the un+1 for various j (Explicit and implicit methods for ordinary differential j equations were discussed in §16.6.) The FTCS ... vol 55, pp 211–246, §2c [3] Kreiss, H.-O 1978, Numerical Methods for Solving Time-Dependent Problems for Partial DifferentialEquations (Montreal: University of Montreal Press), pp 66ff [4] Harten, ... matrix relation F(u) = −v −v ·u (19.1.5) (The physicist-reader may recognize equations (19.1.3) as analogous to Maxwell’s equations for one-dimensional propagation of electromagnetic waves.) We will...
... CBO with temperature are obtained usingEquations (12.32) and (12.33), respectively The change in I C for each temperature is calculated using Equation (12.36) MATLAB Script: % Bias stability % ... CRC Press LLC Solution Equations (12.25), (12.26), and (12.30) can be used to calculate the collector current At each temperature, the stability factors are calculated usingEquations (12.37), (12.39), ... = -1V Assume < V BE < 0.7 V J S = * 10 −10 Solution From Equations (12.1), (12.2) and (12.4), we can write the following MATLAB program MATLAB Script %Input characteristics of a BJT diary ex12_1.dat...
... coefficients an and bn (b) (c) 8.3 Write a MATLAB program to obtain an and bn for n = , 1, , 10 by usingEquations (8.5) and (8.6) Resynthesis g(t) using 10 terms of the values an , bn obtained ... CRC Press LLC 8.3.1 MATLAB function fft The MATLAB function for performing Fast Fourier Transforms is fft ( x ) where x is the vector to be transformed fft ( x , N ) is also MATLAB command that ... u(t ) 2 Using the frequency shifting property of the Fourier Transform, we get G( f ) = 2 + + j 2π ( f − 10) + j 2π ( f + 10) (b, c) The MATLAB program for computing the DFT of MATLAB Script...
... V2 (7.46) Using KCL, we have I = V2 Y2 − I (7.47) Comparing Equations (7.46) and 7.47) to equations (7.35) and (7.36) we have a11 = a 21 = Y2 a12 = a 22 = (7.48) Using the describing equations, ... Bipolar Junction Transistor Solution Using KCL for port 1, V1 = I Z1 (7.32) Using KCL at port 2, we get I = βI + Y2V2 (7.33) Comparing the above two equations to Equations (7.25) and (7.26) we get ... discusses the application of MATLAB for analysis of two-port networks The describing equations for the various two-port network representations are given The use of MATLAB for solving problems involving...
... 16.6 of this chapter treats the subject of stiff equations, relevant both to ordinary differentialequations and also to partial differentialequations (Chapter 19) Sample page from NUMERICAL ... Chapter 16 Integration of Ordinary DifferentialEquations CITED REFERENCES AND FURTHER READING: Gear, C.W 1971, Numerical Initial Value Problems in Ordinary DifferentialEquations (Englewood Cliffs, ... 1973, Computational Methods in Ordinary DifferentialEquations (New York: Wiley) Lapidus, L., and Seinfeld, J 1971, Numerical Solution of Ordinary DifferentialEquations (New York: Academic Press)...