Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
5th Edition
ISBN: 9780321816252
Author: C. Henry Edwards, David E. Penney, David Calvis
Publisher: PEARSON
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Chapter A.5, Problem 13P
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Program Description: Purpose of the problem is to obtain the first three successive approximations for the initial value problem.
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Numerical Methods
Using MatLab through graphical method develop a program that will determine the drag coefficient "c" needed for a parachutists of mass m=68.1kg to have a velocity of 40m/s after free falling for time t=10s. The acceleration due to gravity is 9.8 m/s2.
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Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
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- 6. Two iterative methods for solving linear systems of algebraic equations, Ax = b, are Jacobi and Gauss-Seidel. For each of these methods give necessary and sufficient conditions on A so that the method will give the exact answer in one iteration, regardless of b and the starting value x(0).arrow_forwardUse any programming language for the following: Machine Exercise: a. Make an Algorithm for solving systems of linear algebraic equations using the methods below: 1.) Gauss elimination 2.) LU decomposition method (any one of the following) • Doolittle's decomposition • Crout's decomposition Cholesky's decomposition 3.) Iterative methods (any one of the following) Gauss-Jacobi Gauss-Seidel • Successive Relaxation Conjugate Gradient b. Write a program for solving the system Ax = b by 1.) Gaussian elimination algorithm 2.) LU decomposition methods (any one of the three) %3D • Doolittle's decomposition • Crout's decomposition Cholesky's decompositionarrow_forward5arrow_forward
- 9. Solve the following system of equations by Gauss Elimination method (without pivoting): (v) 2x + 3y -z = 5 4x + 4y - 3z = 3 - 2x + 3y -z = 1 (v) x = 1, y = 2, z = 3 Ans. 10. Solve the following system of equations by Gauss Elimination method (without pivoting): (ui) 5xq − g + g = 10 2x₁ + 4x₂ = 12 *i+ Xg+5£g = −1 Ans. (ui) x1 = 23 9 " ₂x₂ = 31 18 , x3 == 19 18arrow_forwardusing the R applicationarrow_forward8. A parametric equation is given by x= 3t 3t2 (Note that the denominator approaches 0 when t approaches -1) Plot the function (the plot is called the Folium of Descartes) by plotting two curves in the same plot-one y = 1+t3 1+t3 for -30arrow_forwardV Obtain the expression for y(t) which is satisfying the differential equation ÿ + 3y+ 2y = et y(0)=0 and y(0)=0arrow_forwardSuppose that a parachutist with linear drag (m=50 kg, c=12.5kg/s) jumps from an airplane flying at an altitude of a kilometer with a horizontal velocity of 220 m/s relative to the ground. a) Write a system of four differential equations for x,y,vx=dx/dt and vy=dy/dt. b) If theinitial horizontal position is defined as x=0, use Euler’s methods with t=0.4 s to compute the jumper’s position over the first 40 s. c) Develop plots of y versus t and y versus x. Use the plot to graphically estimate when and where the jumper would hit the ground if the chute failed to open.arrow_forward2.) Obtain the solution of the following initial value problem! T' - x =t - 1, T(0) = 0. lourin series of thearrow_forward(Numerical analysis) Here’s a challenging problem for those who know a little calculus. The Newton-Raphson method can be used to find the roots of any equation y(x)=0. In this method, the (i+1)stapproximation,xi+1,toarootofy(x)=0 is given in terms of the ith approximation, xi, by the following formula, where y’ denotes the derivative of y(x) with respect to x: xi+1=xiy(xi)/y(xi) For example, if y(x)=3x2+2x2,theny(x)=6x+2 , and the roots are found by making a reasonable guess for a first approximation x1 and iterating by using this equation: xi+1=xi(3xi2+2xi2)/(6xi+2) a. Using the Newton-Raphson method, find the two roots of the equation 3x2+2x2=0. (Hint: There’s one positive root and one negative root.) b. Extend the program written for Exercise 6a so that it finds the roots of any function y(x)=0, when the function for y(x) and the derivative of y(x) are placed in the code.arrow_forwardignore " Then use Theorem 3.3 in theBurden & Faires textbook to find an error bound for the approximations you obtained but do the rest please with the proper steps and please do not use chat gpt! Thank you !arrow_forwardA circle in the XY-coordinate system is specified by the center coordinates (x, y) and radius (r). Read the values for 2 circles- x1, y1, r1 for C1 and x2, y2, r2 for C2. (i) Determine whether the 2 circles intersect. To solve the problem it suffices to check if the distance between the 2 centers is lesser than the sum of radii of the 2 circles. (ii) Find the smallest circle that encloses the two circles and return its center coordinates and radius. programming language - carrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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