Question 5 (1 mark) Attempt 1 Consider the initial value problem: y'= 4.0(1+42), y(1 Using one...
the answer should be as computer answer Consider the initial value problem: y' = 842+ y(0)=5. (y+5) Using TWO(2) steps of the following explict third order Runge-Kutta scheme ki = hf(nyn), k2 = hf(n+ihgyn+şkı), k3 = hf(en+h,yn+şk2), Yn+1 = yn +4(k1+3k3), obtain an approximate solution to the initial value problem at x = 0.6 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....
674%, y():1 nge- Consider the initial value problem: l- Using TWO(2) steps of the following explict third order Runge-Kutta scheme k1二hj(sn.yn). 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 674%, y():1 nge- Consider the initial value problem: l- Using...
Please have a clear hand writing :) 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 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...
5. Consider the following second order explicit Runge-Kutta scheme: k=hf(an, Yn) k2 = hf(2, +h, yn +ki) Yn+k2. Yn+1 (a) Express the following ordinary differential equation and initial conditions as a sys- tem of first order equations: y(1)=1, /(1) 3. (b) Use the second order explicit Runge-Kutta scheme with one step to compute an approximation to y(1.2). 5. Consider the following second order explicit Runge-Kutta scheme: k=hf(an, Yn) k2 = hf(2, +h, yn +ki) Yn+k2. Yn+1 (a) Express the following...
OU USE 4A14 ILIS MATH2114_1950) Student Test Page - Numerical Question Question 5 (2 marks) Attempt 1 An autonomous system of two first order differential equations can be written as: dy = f(uu), ulto)=u, die = g(u, v), vſto)=vo. A third order explicit Runge-Kutta scheme for an autonomous system of two first order equations is ki = hf(Un, Un), l1 = hg( m, Une) k2 = hf(Wq+şkı,un +şl1). 12 = hg(Un +şk1, 0n +341), k3 = hf(Wn+şk2,vn +şla), 13 =...
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...
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...
Please have a clear hand writing :) 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...
An autonomous system of two first order differential equations can be written as: A third order explicit Runge-Kutta scheme for an autonomous system of two first order equations is hg(un,vn), 63-hf(un+2k2-k㎶n +212-11), 13 hg(un+2k2-ki,un +212-4), t-4 Consider the following second order differential equation, +2dy-7y2-12, with y(0)= 4 and y'(0)=0. dt2 dt Use the Runge-Kutta scheme to find an approximate solution of the second order differential equation, at t = 0.1, if the step size h = 0.05 Maintain at least...