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
Consider the following second order differential equation,
Use the Runge-Kutta scheme to find an approximate solutions of the
second order differential equation, at t = 1.2, if the step size h
= 0.1.
Maintain at least eight decimal digit accuracy throughout all your
calculations.
You may express your answer as a five decimal digit number; for
example 16.17423.
3y2-0.9, with y(1)-0 and y'(1)-1 dt2 dt
Homework Answers
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An autonomous system of two first order differential equations can be written as: A third order...
An autonomous system of two first order differential equations can be written as: A third order e...
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...
A system of two first order differential equations can be written as: A second order explicit R...
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 Consider the following second order differential equation: Use the Runge-kutta scheme to find an approximate solution of the second order differential equation, at x = 0.2, if the step size h = 0.1. Maintain at least eight decimal digit accuracy throughout all your calculations. You may express your answer as a five decimal...
A system of two first order differential equations can be written as 0 dc A second order explicit...
A system of two first order differential equations can be written as 0 dc A second order explicit Runge-Kutta scheme for the system of two first order equations is Consider the following second order differential equation 7+4zy 4, with y(1)-1 and y'(1)--1. Use the Runge-kutta scheme to find an approximate solution of the second order differential equation, at x = 1.2, if the step size h Maintain at least eight decimal digit accuracy throughout all your calculations You may express...
Question 12 (3 marks) Special Attempt 2 A system of two first order differential equations can be written as 0 dr A second order explicit Runge-Kutta scheme for the system of two first order equation...
Question 12 (3 marks) Special Attempt 2 A system of two first order differential equations can be written as 0 dr A second order explicit Runge-Kutta scheme for the system of two first order equations is 1hg(n,un,vn), un+1 Consider the following second order differential equation d2 0cy-6, with v(1)-1 and y'()-o Use the Runge-kutta scheme to find an approximate solution of the second order differential equation, at x = 1.2, if the step size h Maintain at least eight decimal...
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 writing :) Question Question 12 (3 marks) Special Attempt 1 A system of two first order differe...
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...
3. (a) Express the following ordinary differential equation and initial conditions as an autonomous system of...
3. (a) Express the following ordinary differential equation and initial conditions as an autonomous system of first order equations: 2"-223z = 2, '(0)= 1 z(0) 0, (b) Consider the following second order explicit Runge-Kutta scheme written in au- tonomous vector form (y' = f(y)): hf (ynk kihf (yn), k2 yn+1 ynk2. IT Use the second order explicit Runge-Kutta scheme with steplength h compute approximations to z(0.1) and z'(0.1) 0.1 to _
3. (a) Express the following ordinary differential equation and...
OU USE 4A14 ILIS MATH2114_1950) Student Test Page - Numerical Question Question 5 (2 marks) Attempt...
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 =...
5. Consider the following second order explicit Runge-Kutta scheme: k=hf(an, Yn) k2 = hf(2, +h, yn...
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...
3. Consider the following stiff system of autonomous ordinary differential equations du f(u, u) =-3u +3,...
3. Consider the following stiff system of autonomous ordinary differential equations du f(u, u) =-3u +3, u(0)2 = ' dt de g(u, v) -2000u - 1000, v(0)-3 Note that 1 u<2 and -4 <v < 3 for all t. (a) Find the Jacobian matrix for the system of equa tions (b) Find the eigenvalues of the Jacobian matrix. (c) In the figure the shaded region shows the region of absolute stability, in the complex h plane, for third order explicit...
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...
A system of two first order differential equations can be written as 0 dc A second order explicit Runge-Kutta scheme for the system of two first order equations is Consider the following second order differential equation 7+4zy 4, with y(1)-1 and y'(1)--1. Use the Runge-kutta scheme to find an approximate solution of the second order differential equation, at x = 1.2, if the step size h Maintain at least eight decimal digit accuracy throughout all your calculations You may express...
Question 12 (3 marks) Special Attempt 2 A system of two first order differential equations can be written as 0 dr A second order explicit Runge-Kutta scheme for the system of two first order equations is 1hg(n,un,vn), un+1 Consider the following second order differential equation d2 0cy-6, with v(1)-1 and y'()-o Use the Runge-kutta scheme to find an approximate solution of the second order differential equation, at x = 1.2, if the step size h Maintain at least eight decimal...
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
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...
3. (a) Express the following ordinary differential equation and initial conditions as an autonomous system of first order equations: 2"-223z = 2, '(0)= 1 z(0) 0, (b) Consider the following second order explicit Runge-Kutta scheme written in au- tonomous vector form (y' = f(y)): hf (ynk kihf (yn), k2 yn+1 ynk2. IT Use the second order explicit Runge-Kutta scheme with steplength h compute approximations to z(0.1) and z'(0.1) 0.1 to _
3. (a) Express the following ordinary differential equation and...
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 =...
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...
3. Consider the following stiff system of autonomous ordinary differential equations du f(u, u) =-3u +3, u(0)2 = ' dt de g(u, v) -2000u - 1000, v(0)-3 Note that 1 u<2 and -4 <v < 3 for all t. (a) Find the Jacobian matrix for the system of equa tions (b) Find the eigenvalues of the Jacobian matrix. (c) In the figure the shaded region shows the region of absolute stability, in the complex h plane, for third order explicit...
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