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numerical analysis
ANSWER ALL QUESTIONS 1) Suppose we are looking for a solution of the equation:...
5) Suppose we seek a numerical approximation to the solution of the equation:ala sinx 1/2. Estimate...
5) Suppose we seek a numerical approximation to the solution of the equation:ala sinx 1/2. Estimate the number of iterations required to get 100-decimal place accuracy if we solve the equation using a) the Bisection Method (witha= b) Newton's Method, with xo5 c) by iterating Xp+1 = g(xm), with xo =.5 and g(x) = 1 +x- 2 sin(x). - 0,b - 1) In every case, choose the best estimate for the number of iterations from the following five choices: (i)10...
this is numerical analysis QUESTION 1 (a) Apart from 1 = 0 the equation f(1) =...
this is numerical analysis
QUESTION 1 (a) Apart from 1 = 0 the equation f(1) = x2 - 4 sin r = 0 has another root in (1, 2.5). Perform three (10) iterations of the bisection method to approximate the root. State the accuracy of the root after the three iterations. (b) Perform three iterations of Newton's method for the function in (a) above, using x) = 1.5 as the initial (10) solution. Compare the error from the Newton's approximation...
Please answer all questions Q2 2015 a) show that the function f(x) = pi/2-x-sin(x) has at...
Please answer all questions
Q2 2015
a) show that the function f(x) = pi/2-x-sin(x)
has at least one root x* in the interval [0,pi/2]
b)in a fixed-point formulation of the root-finding problem, the
equation f(x) = 0 is rewritten in the equivalent form x = g(x).
thus the root x* satisfies the equation x* = g(x*), and then the
numerical iteration scheme takes the form x(n+1) = g(x(n))
prove that the iterations converge to the root, provided that
the starting...
i need the answer to be on a MatLab window 1. Consider the following equation, which...
i need the answer to be on a MatLab window
1. Consider the following equation, which represents the concentration (c, in mg/ml) of a drug in the bloodstream over time (t, in seconds). Assume we are interested in a concentration of c2 mg/ml C3te-0.4t A. Estimate the times at which the concentration is 2 mg/ml using a graphical method Be sure to show your plot(s). Hint: There are 2 real solutions B. Use MATLAB to apply the secant method (e.g....
this is numerical analysis please do all the questions 1. A function g(x) is called a...
this is numerical analysis please do all the questions
1. A function g(x) is called a contraction on the interval (a,b) if g([a, b]) c [a, b] and moreover, there exists 0 <k < 1 such that væ, y € [a, b] we have 19(x) – 9(y)<k|x – yl. (a) Find d > 0 such that the function g(x) = cos x is a contraction on (0.5 - 4,0.5 + d). Justify fully. Hint: The cosine of 1 radian is...
b) Suppose we wish to find the solution of a nonlinear equation of the form sin(x-0.36)--sin(0.36)e.xo 38 e-x/0.38 Describe briefly how you can use a numerical optimization method to find a solution...
b) Suppose we wish to find the solution of a nonlinear equation of the form sin(x-0.36)--sin(0.36)e.xo 38 e-x/0.38 Describe briefly how you can use a numerical optimization method to find a solution
b) Suppose we wish to find the solution of a nonlinear equation of the form sin(x-0.36)--sin(0.36)e.xo 38 e-x/0.38 Describe briefly how you can use a numerical optimization method to find a solution
(3) Consider the expressions (a) Write down the Runge-Kutta method for the numerical solution to a differential equation Oy (b) Show that if f is independent of y, i.e. f(x, y) g(x) for some g, t...
(3) Consider the expressions (a) Write down the Runge-Kutta method for the numerical solution to a differential equation Oy (b) Show that if f is independent of y, i.e. f(x, y) g(x) for some g, then the Runge-Kutta method on the interval n n + h] becomes Simpson's Rule for the numerical approximation of the integral g(x) dr. In this case, what is the global error, in terms of O(hk) for some k>0?
(3) Consider the expressions (a) Write down...
Need solution for question 5.6 using python? tation to within e, 5.11 Determine the real root...
Need solution for question 5.6 using
python?
tation to within e, 5.11 Determine the real root of x 80: (a) analytically and (b) with the false-position method to within e, = 2.5%. Use initial guesses of 2.0 and 5.0. Compute the estimated error Ea and the true error after each 1.0% teration 5.2 Determine the real root of (x) 5r - 5x2 + 6r -2 (a) Graphically (b) Using bisection to locate the root. Employ initial guesses of 5.12 Given...
(1 point) Suppose that we use Euler's method to approximate the solution to the differential equation...
(1 point) Suppose that we use Euler's method to approximate the solution to the differential equation dyr. dzvi y(0.4) = 9. Let f(x, y) = 25/y. We let Xo = 0.4 and yo = 9 and pick a step size h=0.2. Euler's method is the the following algorithm. From In and Yn, our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing In+1 = xin + h Y n+1 =...
Question 2 Consider the differential equation We saw in class that one solution is the Bessel function (a) Suppose we h...
Question 2 Consider the differential equation We saw in class that one solution is the Bessel function (a) Suppose we have a solution to this ODE in the form y-Σχ0CnXntr where cn 0. By considering the first term of this series show that r must satisfy r2-4-0 (and hence that r = 2 or r =-2) (b) Show that any solution of the form y-ca:0G,2n-2 must satisfy C0 (c) From the theory about singular solutions we know that a linearly...
5) Suppose we seek a numerical approximation to the solution of the equation:ala sinx 1/2. Estimate the number of iterations required to get 100-decimal place accuracy if we solve the equation using a) the Bisection Method (witha= b) Newton's Method, with xo5 c) by iterating Xp+1 = g(xm), with xo =.5 and g(x) = 1 +x- 2 sin(x). - 0,b - 1) In every case, choose the best estimate for the number of iterations from the following five choices: (i)10...
this is numerical analysis
QUESTION 1 (a) Apart from 1 = 0 the equation f(1) = x2 - 4 sin r = 0 has another root in (1, 2.5). Perform three (10) iterations of the bisection method to approximate the root. State the accuracy of the root after the three iterations. (b) Perform three iterations of Newton's method for the function in (a) above, using x) = 1.5 as the initial (10) solution. Compare the error from the Newton's approximation...
Please answer all questions
Q2 2015
a) show that the function f(x) = pi/2-x-sin(x)
has at least one root x* in the interval [0,pi/2]
b)in a fixed-point formulation of the root-finding problem, the
equation f(x) = 0 is rewritten in the equivalent form x = g(x).
thus the root x* satisfies the equation x* = g(x*), and then the
numerical iteration scheme takes the form x(n+1) = g(x(n))
prove that the iterations converge to the root, provided that
the starting...
i need the answer to be on a MatLab window
1. Consider the following equation, which represents the concentration (c, in mg/ml) of a drug in the bloodstream over time (t, in seconds). Assume we are interested in a concentration of c2 mg/ml C3te-0.4t A. Estimate the times at which the concentration is 2 mg/ml using a graphical method Be sure to show your plot(s). Hint: There are 2 real solutions B. Use MATLAB to apply the secant method (e.g....
this is numerical analysis please do all the questions
1. A function g(x) is called a contraction on the interval (a,b) if g([a, b]) c [a, b] and moreover, there exists 0 <k < 1 such that væ, y € [a, b] we have 19(x) – 9(y)<k|x – yl. (a) Find d > 0 such that the function g(x) = cos x is a contraction on (0.5 - 4,0.5 + d). Justify fully. Hint: The cosine of 1 radian is...
b) Suppose we wish to find the solution of a nonlinear equation of the form sin(x-0.36)--sin(0.36)e.xo 38 e-x/0.38 Describe briefly how you can use a numerical optimization method to find a solution
b) Suppose we wish to find the solution of a nonlinear equation of the form sin(x-0.36)--sin(0.36)e.xo 38 e-x/0.38 Describe briefly how you can use a numerical optimization method to find a solution
(3) Consider the expressions (a) Write down the Runge-Kutta method for the numerical solution to a differential equation Oy (b) Show that if f is independent of y, i.e. f(x, y) g(x) for some g, then the Runge-Kutta method on the interval n n + h] becomes Simpson's Rule for the numerical approximation of the integral g(x) dr. In this case, what is the global error, in terms of O(hk) for some k>0?
(3) Consider the expressions (a) Write down...
Need solution for question 5.6 using
python?
tation to within e, 5.11 Determine the real root of x 80: (a) analytically and (b) with the false-position method to within e, = 2.5%. Use initial guesses of 2.0 and 5.0. Compute the estimated error Ea and the true error after each 1.0% teration 5.2 Determine the real root of (x) 5r - 5x2 + 6r -2 (a) Graphically (b) Using bisection to locate the root. Employ initial guesses of 5.12 Given...
(1 point) Suppose that we use Euler's method to approximate the solution to the differential equation dyr. dzvi y(0.4) = 9. Let f(x, y) = 25/y. We let Xo = 0.4 and yo = 9 and pick a step size h=0.2. Euler's method is the the following algorithm. From In and Yn, our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing In+1 = xin + h Y n+1 =...
Question 2 Consider the differential equation We saw in class that one solution is the Bessel function (a) Suppose we have a solution to this ODE in the form y-Σχ0CnXntr where cn 0. By considering the first term of this series show that r must satisfy r2-4-0 (and hence that r = 2 or r =-2) (b) Show that any solution of the form y-ca:0G,2n-2 must satisfy C0 (c) From the theory about singular solutions we know that a linearly...
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