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5. Being able to capture boundary layer effects in fluid dynamics is very important and the grid ...
Project Being able to analytically calculate the solution to a given partial differential equatio...
Project Being able to analytically calculate the solution to a given partial differential equation is often a much more difficult (if not impossible) task than presented here. Possible challenges include irregular domains and strange numerical techniques are often used to approximate the solution to a PDE. The most basic of such methods is the finite difference method. To illustrate the method, consider the Dirchlet Poisson equation in one dimension given by 10:Finite Difference Approximation ary conditions. In those cases, The...
03. Consider the boundary value problem 0 Sts1 y(0) & y(1)-1 where k > 0 is a given real paramete...
03. Consider the boundary value problem 0 Sts1 y(0) & y(1)-1 where k > 0 is a given real parameter a. Verify that y(t) = e-kt (14) is the exact solution of the BVP. b. Use the function mybvp() from the previous problem with h -0.1 and k -10, to solve the BVP by the Finite Difference Method. Plot, on the same axes, the numerical and exact solution. c. Using a log-log plot, graph the maximum error as a function...
Discretization, ODE solving, condition number. Consider the differential equation 5y"(x) - 2y'(x) +10y(x)0 on the interval x E [0,10] with boundary conditions y(0)2 and y (10) 3 we set up a f...
Discretization, ODE solving, condition number. Consider the differential equation 5y"(x) - 2y'(x) +10y(x)0 on the interval x E [0,10] with boundary conditions y(0)2 and y (10) 3 we set up a finite difference scheme as follows. Divide [0,10] into N-10 sub-intervals, i.e. {xo, X1, [0,1,. 10. Denote xi Xo + ih (here, h- 1) and yi E y(x). Approximate the derivatives as follows X10- 2h we have the following equations representing the ODE at each point Xi ,i = 1,...
EECE 4694 Numerical Methods and Computer Applications Homework -5 1. A condenser of capacity C is...
Please use Matlab to solve this problem
EECE 4694 Numerical Methods and Computer Applications Homework -5 1. A condenser of capacity C is discharged through an inductance L and a resistance R in series, and the chargc g at any timc t is given by at2 Given that L-10mH. R-200 ohms. C-0.1μF, and also when 1-0, charge q- 0.01coulomb, and current 0 i. Using finite difference methods for initial value problems, find the value of q from time t0 to...
Exercise 2: Finite element method We are interested in computing numerically the solution to a 2D...
Exercise 2: Finite element method We are interested in computing numerically the solution to a 2D Laplace equation u 0, The triangulated domain is given in the file mesh.mat on Blackboard. which contains the V × 2 nnatrix vertices storing the two coordinates of the vertices and a F × 3 matrix triangles in which each ro w J contains the indices in {1,····V) of the three vertices of the j-th triangle. a) Using for example MATLAB's triplot or trimesh...
I DESPERATELY NEED HELP WITH THIS DIFFERENTIAL EQUATIONS MATLAB ASSIGNMENT IM SUPPOSED TO BE LEARNING BUT...
I DESPERATELY NEED HELP WITH THIS DIFFERENTIAL EQUATIONS MATLAB ASSIGNMENT IM SUPPOSED TO BE LEARNING BUT WE HAVE A SUB AND HE DIDN'T TEACH IT! ITS EULER AND IMPROVED EULER IN MATLAB! HERE IS THE LINK FOR THE IMAGE FILE THAT SHOWS THE FULL INSTRUCTIONS FOR THE CODE. https://imgur.com/a/gjmypLs Also, here is my code so far that I borrowed form an old assignment but the data is all wrong and the application of the code is slightly different so either...
5. The z transform is a very useful tool for studying difference equations. Often difference and ...
5. The z transform is a very useful tool for studying difference equations. Often difference and differential equations are used to describe causal systems and only the causal solution is of interest. This is the "initial condition" problem of a differential equations course. But both difference and differential equations describe more than just the causal system. For instance, "backwards" solutions and "two point boundary value" solutions. One way in which to think about the problem is the ROC of the...
Value for transmissivity is 185，location is B，flow rate is 20 Question 1: No-flow boundary conditions are implemented by: Question 2: Flow Calculation with no abstraction or rech...
Value for transmissivity is 185，location is B，flow rate is
20
Question 1: No-flow boundary conditions are implemented by: Question 2: Flow Calculation with no abstraction or recharge m2/day m/day Condition 1 flow is Condition 2 flow is Question 3: Recharge or abstraction at a node is calculated by: Question 4: Water Level and Flows for Condition 1 are: Water level at pumping/recharge node Flow accross boundary AB Flow accross boundary CD ..,..) is m3/dayFlow accross boundary BC m/dayFlow accross boundary...
Pendulum Clocks Are Very Important...
1. Pendulum clocks are very important for the history of exploration. Accurate time was the best way to determine one's longitude, since the time of sunrise or sunset depends sensitively on your longitude. In this regard, the great enemy of accuracy was thermal expansion of the pendulum used for the chronometer. We are considering a large mass attached at the end of a brass rod. The mass at the end is much greater than the mass of the rod, so we...
roblem 5: When can we neglect axial conduction? Consider steady, fully developed, laminar flow inside a...
roblem 5: When can we neglect axial conduction? Consider steady, fully developed, laminar flow inside a round tube, with the energy equation: The two terms on the right hand side represent conduction effects in the radial and axial directions, respectively. In convection analysis we usually neglect the axial conduction term, resulting in Eq. 8.48. Let's investigate the suitability of this approximation, by comparing the relative magnitudes of those two terms for a tube flow with constant wall temperature The full...
Project Being able to analytically calculate the solution to a given partial differential equation is often a much more difficult (if not impossible) task than presented here. Possible challenges include irregular domains and strange numerical techniques are often used to approximate the solution to a PDE. The most basic of such methods is the finite difference method. To illustrate the method, consider the Dirchlet Poisson equation in one dimension given by 10:Finite Difference Approximation ary conditions. In those cases, The...
03. Consider the boundary value problem 0 Sts1 y(0) & y(1)-1 where k > 0 is a given real parameter a. Verify that y(t) = e-kt (14) is the exact solution of the BVP. b. Use the function mybvp() from the previous problem with h -0.1 and k -10, to solve the BVP by the Finite Difference Method. Plot, on the same axes, the numerical and exact solution. c. Using a log-log plot, graph the maximum error as a function...
Discretization, ODE solving, condition number. Consider the differential equation 5y"(x) - 2y'(x) +10y(x)0 on the interval x E [0,10] with boundary conditions y(0)2 and y (10) 3 we set up a finite difference scheme as follows. Divide [0,10] into N-10 sub-intervals, i.e. {xo, X1, [0,1,. 10. Denote xi Xo + ih (here, h- 1) and yi E y(x). Approximate the derivatives as follows X10- 2h we have the following equations representing the ODE at each point Xi ,i = 1,...
Please use Matlab to solve this problem
EECE 4694 Numerical Methods and Computer Applications Homework -5 1. A condenser of capacity C is discharged through an inductance L and a resistance R in series, and the chargc g at any timc t is given by at2 Given that L-10mH. R-200 ohms. C-0.1μF, and also when 1-0, charge q- 0.01coulomb, and current 0 i. Using finite difference methods for initial value problems, find the value of q from time t0 to...
Exercise 2: Finite element method We are interested in computing numerically the solution to a 2D Laplace equation u 0, The triangulated domain is given in the file mesh.mat on Blackboard. which contains the V × 2 nnatrix vertices storing the two coordinates of the vertices and a F × 3 matrix triangles in which each ro w J contains the indices in {1,····V) of the three vertices of the j-th triangle. a) Using for example MATLAB's triplot or trimesh...
5. The z transform is a very useful tool for studying difference equations. Often difference and differential equations are used to describe causal systems and only the causal solution is of interest. This is the "initial condition" problem of a differential equations course. But both difference and differential equations describe more than just the causal system. For instance, "backwards" solutions and "two point boundary value" solutions. One way in which to think about the problem is the ROC of the...
Value for transmissivity is 185，location is B，flow rate is
20
Question 1: No-flow boundary conditions are implemented by: Question 2: Flow Calculation with no abstraction or recharge m2/day m/day Condition 1 flow is Condition 2 flow is Question 3: Recharge or abstraction at a node is calculated by: Question 4: Water Level and Flows for Condition 1 are: Water level at pumping/recharge node Flow accross boundary AB Flow accross boundary CD ..,..) is m3/dayFlow accross boundary BC m/dayFlow accross boundary...
roblem 5: When can we neglect axial conduction? Consider steady, fully developed, laminar flow inside a round tube, with the energy equation: The two terms on the right hand side represent conduction effects in the radial and axial directions, respectively. In convection analysis we usually neglect the axial conduction term, resulting in Eq. 8.48. Let's investigate the suitability of this approximation, by comparing the relative magnitudes of those two terms for a tube flow with constant wall temperature The full...
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