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Please have a clear hand writing :) Question Question 10 (2 marks) Special Attempt 1 Estimate the solution of the follow...
Please have a clear hand writing :) Question Question 9 (2 marks) Special Attempt 1 y(0) 3. Consider the initial value p...
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Question Question 9 (2 marks) Special Attempt 1 y(0) 3. Consider the initial value problem: l Using Euler's method: yn+1ynthy n+1tn+h, with step-size h 0.05, obtain an approximate solution to the initial value problem at x- 0.1 Maintain at least eight decimal digit accuracy throughout all calculations You may express your answer as a five decimal digit number; for example 6.27181. YOU DO NOT HAVE TO ROUND YOUR FINAL ESTIMATE Estimate at x0.1...
Please have a clear hand writing :) Question Question 9 (2 marks) Special Attempt 1 y(0)...
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Question Question 9 (2 marks) Special Attempt 1 y(0) 3. Consider the initial value problem: l Using Euler's method: yn+1ynthy n+1tn+h, with step-size h 0.05, obtain an approximate solution to the initial value problem at x- 0.1 Maintain at least eight decimal digit accuracy throughout all calculations You may express your answer as a five decimal digit number; for example 6.27181. YOU DO NOT HAVE TO ROUND YOUR FINAL ESTIMATE Estimate at x0.1...
Please have a clear hand writing :) Question Question 3 (2 marks) Special Attempt 1 Use three iterations of the secant m...
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Question Question 3 (2 marks) Special Attempt 1 Use three iterations of the secant method to find an approximate solution of the equation e-2.1x-5s-20 if your initial estimates are x0 3.65 and x1 3.9 Maintain at least eight digits throughout all your calculations. When entering your final result you MAY round your estimate to five decimal digit accuracy. For example 1.67353 YOU DO NOT HAVE TO ROUND YOUR FINAL ESTIMATE. X4= Skipped
Question...
Please have a clear hand writing :) Question Question 11 (2 marks) Special Attempt 1 (r+5 Consider the initial value pro...
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Question Question 11 (2 marks) Special Attempt 1 (r+5 Consider the initial value problem: u'ー(EN) e-2x· y(0)=5. Using TWO(2) steps of the following explict third order Runge-Kutta scheme k3), 7t obtain an approximate solution to the initial value problem at x 0.2 Maintain at least eight decimal digit accuracy throughout all your calculations You may express your answer as a single five decimal digit number, for example 17.18263. YOU DO NOT HAVE TO...
Question 4 (1 mark) Attempt 1 Estimate the solution of the following first order autonomous system...
Question 4 (1 mark) Attempt 1 Estimate the solution of the following first order autonomous system at t-1.2 using two steps of Euler's method with step-size h 0.1 Maintain at least eight decimal digit accuracy throughout all your calculations. You may express your answers as five decimal digit numbers; for example 3.17423. YOU DO NOT HAVE TO ROUND YOUR FINAL ESTIMATES.
Please have a clear hand writing :) Question Question 12 (3 marks) Special Attempt 1 A system of two first order differe...
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Question Question 12 (3 marks) Special Attempt 1 A system of two first order differential equations can be written as A second order explicit Runge-Kutta scheme for the system of two first order equations is n+l Vn +12 Consider the following second order differential equation 4 d9-' with y(1)-4 and y'(1)-1 a.n Use the Runge-kutta scheme to find an approximate solution of the second order differential equation, at x = 1.4, if the...
Please have a clear hand writing :) Question Question 2 (2 marks) Special Attempt 1 Apply three iterations of Newton'...
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Question Question 2 (2 marks) Special Attempt 1 Apply three iterations of Newton's method to find an approximate solution of the equation e1.6x = 1.9 +1.3cos2x if your initial estimate is xo 1.1 Maintain at least eight digits throughout all your calculations. When entering your final result you MAY round your estimate to five decimal digit accuracy. For example 1.67353 YOU DO NOT HAVE TO ROUND YOUR FINAL ESTIMATE. x3Skipped
Question Question 2...
Question Question 9 (2 marks) Attempt 1 Consider the initial value problem: v=2x2+5 y(1) = 3....
Question Question 9 (2 marks) Attempt 1 Consider the initial value problem: v=2x2+5 y(1) = 3. Using Euler's method: yn+1 =y, thyn n+1 = In th, with step-size h = 0.5, obtain an approximate solution to the initial value problem at x = 2. Maintain at least eight decimal digit accuracy throughout all calculations. You may express your answer as a five decimal digit number, for example 6.27181 YOU DO NOT HAVE TO ROUND YOUR FINAL ESTIMATE. Estimate at x...
Question 11 (2 marks) Special Attempt 2 I value problem: y'4y+3 Consider the initial value problem: y'-43 Using TWO(2) steps of the following explict third order Runge-Kutta scheme 1hyn 2 obt...
Question 11 (2 marks) Special Attempt 2 I value problem: y'4y+3 Consider the initial value problem: y'-43 Using TWO(2) steps of the following explict third order Runge-Kutta scheme 1hyn 2 obtain an approximate solution to the initial value problem at x 0.04. Maintain at least eight decimal digit accuracy throughout all your calculations. You may express your answer as a single five decimal digit number, for example 17.18263. YOU DO NOT HAVE TO ROUND YOUR FINAL ESTIMATE. y(0.04) Skipped
Question...
Please find y(1.4) Question Question 12 (3 marks) Special Attempt 1 A system of two first order differential equations c...
Please find y(1.4)
Question Question 12 (3 marks) Special Attempt 1 A system of two first order differential equations can be written as A second order explicit Runge-Kutta scheme for the system of two first order equations is k1hn,un,vn), un+1 Consider the following second order differential equation d-y + 2 y-9y with y(1) and y'(1) 4 1. , Use the Runge-kutta scheme to find an approximate solution of the second order differential equation, at x-1.4, if the step size h...
Please have a clear hand
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Question Question 9 (2 marks) Special Attempt 1 y(0) 3. Consider the initial value problem: l Using Euler's method: yn+1ynthy n+1tn+h, with step-size h 0.05, obtain an approximate solution to the initial value problem at x- 0.1 Maintain at least eight decimal digit accuracy throughout all calculations You may express your answer as a five decimal digit number; for example 6.27181. YOU DO NOT HAVE TO ROUND YOUR FINAL ESTIMATE Estimate at x0.1...
Please have a clear hand
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Question Question 9 (2 marks) Special Attempt 1 y(0) 3. Consider the initial value problem: l Using Euler's method: yn+1ynthy n+1tn+h, with step-size h 0.05, obtain an approximate solution to the initial value problem at x- 0.1 Maintain at least eight decimal digit accuracy throughout all calculations You may express your answer as a five decimal digit number; for example 6.27181. YOU DO NOT HAVE TO ROUND YOUR FINAL ESTIMATE Estimate at x0.1...
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Question Question 3 (2 marks) Special Attempt 1 Use three iterations of the secant method to find an approximate solution of the equation e-2.1x-5s-20 if your initial estimates are x0 3.65 and x1 3.9 Maintain at least eight digits throughout all your calculations. When entering your final result you MAY round your estimate to five decimal digit accuracy. For example 1.67353 YOU DO NOT HAVE TO ROUND YOUR FINAL ESTIMATE. X4= Skipped
Question...
Please have a clear hand
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Question Question 11 (2 marks) Special Attempt 1 (r+5 Consider the initial value problem: u'ー(EN) e-2x· y(0)=5. Using TWO(2) steps of the following explict third order Runge-Kutta scheme k3), 7t obtain an approximate solution to the initial value problem at x 0.2 Maintain at least eight decimal digit accuracy throughout all your calculations You may express your answer as a single five decimal digit number, for example 17.18263. YOU DO NOT HAVE TO...
Question 4 (1 mark) Attempt 1 Estimate the solution of the following first order autonomous system at t-1.2 using two steps of Euler's method with step-size h 0.1 Maintain at least eight decimal digit accuracy throughout all your calculations. You may express your answers as five decimal digit numbers; for example 3.17423. YOU DO NOT HAVE TO ROUND YOUR FINAL ESTIMATES.
Please have a clear hand
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Question Question 12 (3 marks) Special Attempt 1 A system of two first order differential equations can be written as A second order explicit Runge-Kutta scheme for the system of two first order equations is n+l Vn +12 Consider the following second order differential equation 4 d9-' with y(1)-4 and y'(1)-1 a.n Use the Runge-kutta scheme to find an approximate solution of the second order differential equation, at x = 1.4, if the...
Please have a clear hand
writing :)
Question Question 2 (2 marks) Special Attempt 1 Apply three iterations of Newton's method to find an approximate solution of the equation e1.6x = 1.9 +1.3cos2x if your initial estimate is xo 1.1 Maintain at least eight digits throughout all your calculations. When entering your final result you MAY round your estimate to five decimal digit accuracy. For example 1.67353 YOU DO NOT HAVE TO ROUND YOUR FINAL ESTIMATE. x3Skipped
Question Question 2...
Question Question 9 (2 marks) Attempt 1 Consider the initial value problem: v=2x2+5 y(1) = 3. Using Euler's method: yn+1 =y, thyn n+1 = In th, with step-size h = 0.5, obtain an approximate solution to the initial value problem at x = 2. Maintain at least eight decimal digit accuracy throughout all calculations. You may express your answer as a five decimal digit number, for example 6.27181 YOU DO NOT HAVE TO ROUND YOUR FINAL ESTIMATE. Estimate at x...
Question 11 (2 marks) Special Attempt 2 I value problem: y'4y+3 Consider the initial value problem: y'-43 Using TWO(2) steps of the following explict third order Runge-Kutta scheme 1hyn 2 obtain an approximate solution to the initial value problem at x 0.04. Maintain at least eight decimal digit accuracy throughout all your calculations. You may express your answer as a single five decimal digit number, for example 17.18263. YOU DO NOT HAVE TO ROUND YOUR FINAL ESTIMATE. y(0.04) Skipped
Question...
Please find y(1.4)
Question Question 12 (3 marks) Special Attempt 1 A system of two first order differential equations can be written as A second order explicit Runge-Kutta scheme for the system of two first order equations is k1hn,un,vn), un+1 Consider the following second order differential equation d-y + 2 y-9y with y(1) and y'(1) 4 1. , Use the Runge-kutta scheme to find an approximate solution of the second order differential equation, at x-1.4, if the step size h...
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