solving differential equations using matlab

... Generating Blend Surfaces Using Partial Differential Equations 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...

Ngày tải lên: 13/08/2014, 23:20

Ngày tải lên: 19/10/2013, 20:15

... 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...

Ngày tải lên: 23/10/2013, 16:15

Ngày tải lên: 23/10/2013, 18:15

... Okyere Matlab Fundamentals.” Electronics and Circuit Analysis using MATLAB Ed John Okyere Attia Boca Raton: CRC Press LLC, 1999 © 1999 by CRC PRESS LLC CHAPTER ONE MATLAB FUNDAMENTALS MATLAB ... with simple, easy, hands-on introduction to MATLAB; (2) to demonstrate the use of MATLAB for solving electronics problems; (3) to show the various ways MATLAB can be used to solve circuit analysis ... The book is divided into three parts: Introduction to MATLAB, Circuit analysis applications using MATLAB, and electronics applications with MATLAB It is recommended that the reader work through...

Ngày tải lên: 27/10/2013, 23:15

... 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,...

Ngày tải lên: 27/10/2013, 23:15

... 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, Edition, ... graph may be specified using the statement: plot(x, y, ’g’) © 1999 CRC Press LLC implying, plot x versus y using green color Line and mark style may be added to color type using the command plot(x, ... PLOTTING COMMANDS 2.1 GRAPH FUNCTIONS MATLAB has built-in functions that allow one to generate bar charts, x-y, polar, contour and 3-D plots, and bar charts MATLAB also allows one to give titles...

Ngày tải lên: 27/10/2013, 23:15

... 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...

Ngày tải lên: 28/10/2013, 22:15

... obtained in the time domain This normally involves solving differential equations By transforming the differential equations into algebraic equations using phasors or complex frequency representation, ... can compute the vector [v] using the MATLAB command V = inv(Y ) * I where inv(Y ) is the inverse of the matrix [Y ] A MATLAB program for solving V3 is as follows: MATLAB Script diary ex6_2.dat ... response The magnitude and phase characteristics can be obtained using MATLAB function freqs © 1999 CRC Press LLC 6.4.1 MATLAB function freqs MATLAB function freqs is used to obtain the frequency response...

Ngày tải lên: 06/11/2013, 09:15

... useful for solving RLC circuit problems From the RLC circuit, we write differential equations by using network analysis tools The differential equations are converted into algebraic equations using ...   i1    (5.40) MATLAB functions for solving ordinary differential equations are ODE functions These are described in the following section 5.4.1 MATLAB Ode Functions MATLAB has two functions, ... containing the above differential equations MATLAB Script % % solution of a set of first order differential equations % the function diff3(t,v) is created to evaluate % the differential equation...

Ngày tải lên: 06/11/2013, 09:15

... 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) Using Equations (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...

Ngày tải lên: 06/11/2013, 09:15

... 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 Differential Equations (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...

Ngày tải lên: 07/11/2013, 19:15

Ngày tải lên: 12/12/2013, 07:15

... CBO with temperature are obtained using Equations (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 using Equations (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...

Ngày tải lên: 13/12/2013, 01:15

... Configuration © 1999 CRC Press LLC Solution Using voltage division sC1 V1 ( s) = V IN R1 + sC1 (11.26) From Equation (11.24) VO R2 ( s) = + sC2 V1 (11.27) Using Equations (11.26 ) and (11.27), we have ... (b) Differential- mode Gain Acm , is defined as vo vi ,cm Acm = The differential- mode gain, Ad = (11.59) Ad , is defined as vo vid (11.60) For an op amp with arbitrary input voltages, the differential ... R1 = VIN − V1 VIN − V0 A = R1 R1 i = 0, we have (11.31) (11.32) Also VO = V1 − I R R2 (11.33) Using Equations (11.30), (11.31) and (11.32), Equation (11.33) becomes VO = − VO R2 − (V + VO A) A...

Ngày tải lên: 13/12/2013, 01:15

... profile © 1999 CRC Press LLC Solution Using Equations (10.38) and (10.59), we write the MATLAB program to obtain the diffusion and depletion capacitance MATLAB Script % % Diffusion and depletion ...  N A   ln = q q  ni  (10.34) and Using Equations (10.31) to (10.34), we have VC = kT  N A N D   ln q  ni2  (10.35) It should be noted that Equations (10.30) and (10.35) are identical ... obtained from Equations (10.53) and (10.54) by setting VS equal to zero Equations (10.53 to 10.55) are, strictly speaking, valid under the conditions of reversed-biased VS < The equations can,...

Ngày tải lên: 13/12/2013, 01:15

... RT I + VZ Equations (9.53) and (9.56) are two linear equations solving for (9.56) I, so we get VZ = VT − RT I = −20 + 0.05I ⇒ © 1999 CRC Press LLC I= (VT + 20) RT + 0.05 (9.57) From Equations ... = 1mA and VD1 = 0.7 V Using Equation (9.10), I D2 is calculated by I D2 = VDC − VD1 R Using Equation (9.15), V D2 is calculated by I 2 VD = VD1 + nVT ln D   I D1  Using Equation (9.10), ... technique is particularly facilitated by using computers Example 9.4 illustrates the use of MATLAB for doing the iteration technique Example 9.4 Redo Example 9.3 using the iterative technique The iteration...

Ngày tải lên: 13/12/2013, 01:15

... coefficients an and bn (b) (c) 8.3 Write a MATLAB program to obtain an and bn for n = , 1, , 10 by using Equations (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...

Ngày tải lên: 13/12/2013, 01:15

... 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...

Ngày tải lên: 13/12/2013, 01:15

... 16.6 of this chapter treats the subject of stiff equations, relevant both to ordinary differential equations and also to partial differential equations (Chapter 19) Sample page from NUMERICAL ... Chapter 16 Integration of Ordinary Differential Equations CITED REFERENCES AND FURTHER READING: Gear, C.W 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, ... 1973, Computational Methods in Ordinary Differential Equations (New York: Wiley) Lapidus, L., and Seinfeld, J 1971, Numerical Solution of Ordinary Differential Equations (New York: Academic Press)...

Ngày tải lên: 15/12/2013, 04:15