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Please have a clear hand writing :) Question Question 14 (1 mark) Special Attempt 1 Consider the following system of aut...
Please have a clear hand writing :) Question Question 10 (2 marks) Special Attempt 1 Estimate the solution of the follow...
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Question Question 10 (2 marks) Special Attempt 1 Estimate the solution of the following first order autonomous system at t-0.02 using two steps of Euler's method with step-size h 0.01: du dt 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. v(0.02)Skipped u(0.02) Skipped
Question Question 10 (2 marks)...
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...
Question Question 1 (1 mark) Attempt 1 Consider the boundary value problem: du+ U=1, 2<c<13 with...
Question Question 1 (1 mark) Attempt 1 Consider the boundary value problem: du+ U=1, 2<c<13 with u(2) = 4 and u(13) = 5 Find functions g and , such that u=gta, is a quadratic approximation that satisfies the boundary conditions. Your answer should consist of two expressions, the first representing the term g and the second representing the term ,. Both should be expressed in terms of the independent variable x. Your answers should be expressed as a function of...
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...
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...
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...
Question 1 (1 mark) Attempt 1 Consider the boundary value problem1, 2<8 with uç2)-3 and uB)-s...
Question 1 (1 mark) Attempt 1 Consider the boundary value problem1, 2<8 with uç2)-3 and uB)-s Find functions g and фі such that u gtal +1 is a quadratic approximation that satisfies the boundary condos. Your answer should consist of two expressions, the frst representing the term g and the second representing the term ti. Both shouild be expressed in terms of tho independent varatbie Your answers should be expressed as a function of x using the correct syntax For...
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...
Pleas have a clear hand writing :) Question Question 6 (1 mark) Attempt 1 Evaluate the line integral: (1,3,5) (8ysinh(4x...
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Question Question 6 (1 mark) Attempt 1 Evaluate the line integral: (1,3,5) (8ysinh(4x)+62) dx+(2cosh(4x)+5z2) dy+(10yz+6x) dz. (0,1,1) Your answer can be expressed as number accurate to five significant figures or as an expression in correct Maple syntax. For example: 5*cosh(13)/7+3*(2^5)/11 OR 15.91845987 OR rounded to 15.918 |Skipped
Question Question 6 (1 mark) Attempt 1 Evaluate the line integral: (1,3,5) (8ysinh(4x)+62) dx+(2cosh(4x)+5z2) dy+(10yz+6x) dz. (0,1,1) Your answer can be expressed as number accurate to...
Question 3 (1 mark) Special Attempt 1 When solving a particular boundary value problem using the...
Question 3 (1 mark) Special Attempt 1 When solving a particular boundary value problem using the approximate solution u(x)=C–1+Q1 (32-40) the residual is R(*)= 3+20–42+Q7 (22+50+1). Use the collocation method with the collocation point x = 2 to find the value of a Your answer should consist of the single (exact) value of Qy. For example -911/203 Qq = Skipped
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Question Question 10 (2 marks) Special Attempt 1 Estimate the solution of the following first order autonomous system at t-0.02 using two steps of Euler's method with step-size h 0.01: du dt 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. v(0.02)Skipped u(0.02) Skipped
Question Question 10 (2 marks)...
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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...
Question Question 1 (1 mark) Attempt 1 Consider the boundary value problem: du+ U=1, 2<c<13 with u(2) = 4 and u(13) = 5 Find functions g and , such that u=gta, is a quadratic approximation that satisfies the boundary conditions. Your answer should consist of two expressions, the first representing the term g and the second representing the term ,. Both should be expressed in terms of the independent variable x. Your answers should be expressed as a function of...
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...
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...
Please have a clear hand
writing :)
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...
Question 1 (1 mark) Attempt 1 Consider the boundary value problem1, 2<8 with uç2)-3 and uB)-s Find functions g and фі such that u gtal +1 is a quadratic approximation that satisfies the boundary condos. Your answer should consist of two expressions, the frst representing the term g and the second representing the term ti. Both shouild be expressed in terms of tho independent varatbie Your answers should be expressed as a function of x using the correct syntax For...
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...
Pleas have a clear hand
writing :)
Question Question 6 (1 mark) Attempt 1 Evaluate the line integral: (1,3,5) (8ysinh(4x)+62) dx+(2cosh(4x)+5z2) dy+(10yz+6x) dz. (0,1,1) Your answer can be expressed as number accurate to five significant figures or as an expression in correct Maple syntax. For example: 5*cosh(13)/7+3*(2^5)/11 OR 15.91845987 OR rounded to 15.918 |Skipped
Question Question 6 (1 mark) Attempt 1 Evaluate the line integral: (1,3,5) (8ysinh(4x)+62) dx+(2cosh(4x)+5z2) dy+(10yz+6x) dz. (0,1,1) Your answer can be expressed as number accurate to...
Question 3 (1 mark) Special Attempt 1 When solving a particular boundary value problem using the approximate solution u(x)=C–1+Q1 (32-40) the residual is R(*)= 3+20–42+Q7 (22+50+1). Use the collocation method with the collocation point x = 2 to find the value of a Your answer should consist of the single (exact) value of Qy. For example -911/203 Qq = Skipped
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