Homework Answers
Part C is right.
For the given equation its better to use Finite difference method, it will converta the equation in algebric equations or in matrix form. And also we can include the Neumann boundary condition in the equation.
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Question 24 1 pts Using the shooting method for the following second-order differential equation governing the...
Question 25 1 pts Using the shooting method for the following second-order differential equation governing the...
Question 25 1 pts Using the shooting method for the following second-order differential equation governing the boundary value problem G.E: + EA (c) a + 2 = L(x) * € (0,L] B.C's: u (0) = 0 and EA (x) din le=L= F. An appropriate algebraic equation to use in the finite difference of the boundary condition at = Lis There is no suitable finite difference equation that can be obtained. u(L) - u (L - Ax) F.A BAL) None of...
Question 19 Using the shooting method for the following second-order differential equation governing the boundary value...
Question 19 Using the shooting method for the following second-order differential equation governing the boundary value problem G.E: + EA () 9 + - =D () 2 € (0,L] B.C's:u (0) = 0 and EA (2) --=F. An appropriate algebraic equation to use in the finite difference solution of the boundary value problem posed in question 24 is -Post A)u(L) - (L+Ax) EAL) F. 201 B) Su (L) - u(L - Ax) + 4u (L + A2) EAL C) (L)...
Problem 5. Consider the following second order linear differential equation f"(t)-f'(t) +f(t) kt ...
Problem 5. Consider the following second order linear differential equation f"(t)-f'(t) +f(t) kt which models a forced oscillation in a damping material. For example, imagine moving your hand back and forth underwater. Write this equation as a set of coupled first order equations by doing the following: ·Define a new function g = f'(t). This gives you one of the two coupled equations. . Use the given ODE, g, and its derivatives to write the second first order equation. Both...
L-8 29 -15 22] 111 4 3 2 1 10. The differential equations of high order: 2 And boundary conditions fo)-0, f' (0)-0, f'(5)-1, g(o)-1.5, g(5)-1 Can be solved using The Shooting-Newton-Raphson a...
L-8 29 -15 22] 111 4 3 2 1 10. The differential equations of high order: 2 And boundary conditions fo)-0, f' (0)-0, f'(5)-1, g(o)-1.5, g(5)-1 Can be solved using The Shooting-Newton-Raphson and multivariable Runge-Kutta for a value of (y-1.7), re write the system of equations in the canonical form (i.e. as a set of ODES of first order and its boundary conditions). It is not required to solve the equations, just list the system of first order differential equations...
Problem #4. The convective heat transfer problem of cold oil flowing over a hot surface can...
Problem #4. The convective heat transfer problem of cold oil flowing over a hot surface can be described by the following second-order ordinary differential equations. d'T dT +0.83x = 0 dx? dx T(0)=0 (1) T(5)=1 where T is the dimensionless temperature and x is the dimensionless similarity variable. This is a boundary-value problem with the two conditions given on the wall (x=0, T(O) = 0) and in the fluid far away from the wall (x = 5, T(5) = 1)....
Problem #4. The convective heat transfer problem of cold oil flowing over a hot surface can...
Problem #4. The convective heat transfer problem of cold oil flowing over a hot surface can be described by the following second-order ordinary differential equations. der 0 dx T(0)=0 (1) T(5)=1 where T is the dimensionless temperature and x is the dimensionless similarity variable. dr? +0.83, dT This is a boundary-value problem with the two conditions given on the wall (x=0, T(O) = 0) and in the fluid far away from the wall (x = 5,7/5) = 1). You are...
Find the general solution of the first order partial differential equation using the method of separation...
Find the general solution of the first order partial differential equation using the method of separation of variables. Use the substitution U = XY to solve the boundary value partial differential equation 34x + 2 uy = u for . for u(0,y) = 2e By Use the substitution U = XY to solve the boundary value partial differential equation 3ux +2y = for 3. for u(x,0) = 4e2+ +5e*:
Problem #3: The Ralston method is a second-order method that can be used to solve an...
Problem #3: The Ralston method is a second-order method that can be used to solve an initial-value, first-orde ordinary differential equation. The algorithm is given below: Vi#l=>: +($k+ş kz)h Where ky = f(ti,y:) * = f(mehr) You are asked to do the following: 3.1 Following that given in Inclass activity #10a, develop a MATLAB function to implement the algorithm for any given function, the time span, and the initial value. 3.2 Use your code to solve the following first-order ordinary...
Problem #3: The Ralston method is a second-order method that can be used to solve an...
Problem #3: The Ralston method is a second-order method that can be used to solve an initial-value, first-order ordinary differential equation. The algorithm is given below: 2 Yi+1 = yi + k +k2)h Where kı = f(ti,y;) 3 k2 = ft;+ -h, y; +-kih You are asked to do the following: 3.1 Following that given in Inclass activity #10a, develop a MATLAB function to implement the algorithm for any given function, the time span, and the initial value. 3.2 Use...
Find the value of x(0.5) for the initial value problem at = thx(0)=1 using Euler's method with step size h 0.05 Find the value of x(0.4) for the coupled first order differential equations toge...
Find the value of x(0.5) for the initial value problem at = thx(0)=1 using Euler's method with step size h 0.05 Find the value of x(0.4) for the coupled first order differential equations together with initial conditions with step size 0.1: 2. dt t+x 3. dx dt = y, dy dt x(0) = 1.2 and --ty +xt2 + y(o) 0.8
Find the value of x(0.5) for the initial value problem at = thx(0)=1 using Euler's method with step size h...
Question 25 1 pts Using the shooting method for the following second-order differential equation governing the boundary value problem G.E: + EA (c) a + 2 = L(x) * € (0,L] B.C's: u (0) = 0 and EA (x) din le=L= F. An appropriate algebraic equation to use in the finite difference of the boundary condition at = Lis There is no suitable finite difference equation that can be obtained. u(L) - u (L - Ax) F.A BAL) None of...
Question 19 Using the shooting method for the following second-order differential equation governing the boundary value problem G.E: + EA () 9 + - =D () 2 € (0,L] B.C's:u (0) = 0 and EA (2) --=F. An appropriate algebraic equation to use in the finite difference solution of the boundary value problem posed in question 24 is -Post A)u(L) - (L+Ax) EAL) F. 201 B) Su (L) - u(L - Ax) + 4u (L + A2) EAL C) (L)...
Problem 5. Consider the following second order linear differential equation f"(t)-f'(t) +f(t) kt which models a forced oscillation in a damping material. For example, imagine moving your hand back and forth underwater. Write this equation as a set of coupled first order equations by doing the following: ·Define a new function g = f'(t). This gives you one of the two coupled equations. . Use the given ODE, g, and its derivatives to write the second first order equation. Both...
L-8 29 -15 22] 111 4 3 2 1 10. The differential equations of high order: 2 And boundary conditions fo)-0, f' (0)-0, f'(5)-1, g(o)-1.5, g(5)-1 Can be solved using The Shooting-Newton-Raphson and multivariable Runge-Kutta for a value of (y-1.7), re write the system of equations in the canonical form (i.e. as a set of ODES of first order and its boundary conditions). It is not required to solve the equations, just list the system of first order differential equations...
Problem #4. The convective heat transfer problem of cold oil flowing over a hot surface can be described by the following second-order ordinary differential equations. d'T dT +0.83x = 0 dx? dx T(0)=0 (1) T(5)=1 where T is the dimensionless temperature and x is the dimensionless similarity variable. This is a boundary-value problem with the two conditions given on the wall (x=0, T(O) = 0) and in the fluid far away from the wall (x = 5, T(5) = 1)....
Problem #4. The convective heat transfer problem of cold oil flowing over a hot surface can be described by the following second-order ordinary differential equations. der 0 dx T(0)=0 (1) T(5)=1 where T is the dimensionless temperature and x is the dimensionless similarity variable. dr? +0.83, dT This is a boundary-value problem with the two conditions given on the wall (x=0, T(O) = 0) and in the fluid far away from the wall (x = 5,7/5) = 1). You are...
Find the general solution of the first order partial differential equation using the method of separation of variables. Use the substitution U = XY to solve the boundary value partial differential equation 34x + 2 uy = u for . for u(0,y) = 2e By Use the substitution U = XY to solve the boundary value partial differential equation 3ux +2y = for 3. for u(x,0) = 4e2+ +5e*:
Problem #3: The Ralston method is a second-order method that can be used to solve an initial-value, first-orde ordinary differential equation. The algorithm is given below: Vi#l=>: +($k+ş kz)h Where ky = f(ti,y:) * = f(mehr) You are asked to do the following: 3.1 Following that given in Inclass activity #10a, develop a MATLAB function to implement the algorithm for any given function, the time span, and the initial value. 3.2 Use your code to solve the following first-order ordinary...
Problem #3: The Ralston method is a second-order method that can be used to solve an initial-value, first-order ordinary differential equation. The algorithm is given below: 2 Yi+1 = yi + k +k2)h Where kı = f(ti,y;) 3 k2 = ft;+ -h, y; +-kih You are asked to do the following: 3.1 Following that given in Inclass activity #10a, develop a MATLAB function to implement the algorithm for any given function, the time span, and the initial value. 3.2 Use...
Find the value of x(0.5) for the initial value problem at = thx(0)=1 using Euler's method with step size h 0.05 Find the value of x(0.4) for the coupled first order differential equations together with initial conditions with step size 0.1: 2. dt t+x 3. dx dt = y, dy dt x(0) = 1.2 and --ty +xt2 + y(o) 0.8
Find the value of x(0.5) for the initial value problem at = thx(0)=1 using Euler's method with step size h...
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