Question about MATLAB boundary value problem.
How can I solve the following problems? I would appreciate if you could briefly explain how you get the answer. (In the second problem, the selected answer is not correct.)

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Question about MATLAB boundary value problem. How can I solve the following problems? I would appreciate...
write MATLAB scripts to solve differential equations.
Computing 1: ELE1053 Project 3E:Solving Differential Equations Project Principle Objective: Write MATLAB scripts to solve differential equations. Implementation: MatLab is an ideal environment for solving differential equations. Differential equations are a vital tool used by engineers to model, study and make predictions about the behavior of complex systems. It not only allows you to solve complex equations and systems of equations it also allows you to easily present the solutions in graphical form....
Problem 4: Suppose that the movement of rush-hour traffic on a typical expresswa be modeled using the differential equation du du where u(x) is the density of cars (vehicles per mile), and a is distance miles) in the direction of traffic flow. We w to the boundary conditions ant to solve this equation subject u(0) 300, u(5) 400. a) Use second-order accurate, central-difference approximations to discretize the differential equation and write down the finite-difference equation for a typical point zi...
Consider the following boundary value problem: du du dx dx u=-e* sin(x) Discretize the ODE using backward second-order accurate scheme for both derivatives. The second order finite accuracy difference for the derivatives are given by: 2h (3)-1(1,2)-45 (7.1)+31(x) 8 (*)== (4.5) +41 (1.2) -51 (3.1) +2f (x) h?
Question (2.5)
In Problems 2.4-2.9, construct the weak forms and, whenever possible, the associated quadratic functionals (I). A linear differential equation: 2.4 du + u x dx dx du u(0) =1, dx =2 2.5 A nonlinear equation: du +f=0 for 0 <x<1 dx dx dx = 0 u(1)-V2
In Problems 2.4-2.9, construct the weak forms and, whenever possible, the associated quadratic functionals (I). A linear differential equation: 2.4 du + u x dx dx du u(0) =1, dx =2 2.5...
In this problem we explore using Fourier series to solve nonhomogeneous boundary value problems. For un type un, for derivatives use the prime notation u′n,u′′n,…. Solve the heat equation ∂2u∂x2+2e−4t=∂u∂t,00 u(0,t)=0,u(5,t)=0,t>0 u(x,0)=3,0
Consider in x [0, L], the second order Boundary Value Problem lu where qra+bx. The solution is subject to the boundary conditions du dxl Find an approximate solution using the using a three-node element. The shape function of the element is, in a local coordinate system s E[, Thus local node number 1 is to the left (s--1) and number 2 is in centre (s -0) and the third node is to the right (s 1) Hint: Assume that the...
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)....
Please don’t copy from another answer I need clear
solution
2-15. To illustrate ..boundary-layer" behavior, i.e., the effect of the no-slip condition for large Reynolds numbers, Prandtl in a 1932 lecture proposed the following model (lin- ear) differential equation: du du dy where e mimics the smal viscosity of the fluid. The boundary conditions are (1) u(0) 2, and (2) u remains bounded as y becomes large. Solve this equation for these conditions and plot the profile u(y) in the...
1. Second order linear boundary value problems: Discuss the solution process for a linear boundary value problem of the form u" (x) + g(x)u, (x) + h (x)u(x) = f(x), -u,(a) + u (a) = α, u,(b) + u(b) = β a. a < x < b where a, b E R with a < b, g(x), h(x) and f(x) are given functions, and α, β E R b. The funconsux) and u2(x) solve the differential equation u"(x) +g(x)u'(x) +...
11. Solve this boundary value problem for u(x, t): n2 xu,-(x14),--11 (0<x <c,0 11 (c, 1) = 0, u(x, 0) = f(x), where u is continuous for0sxc,0 and where n is a positive integer. Answer: u(x, 1) Σ A,Jn(gjx) exp (-α,1), where a", and A, are the constants j-1
11. Solve this boundary value problem for u(x, t): n2 xu,-(x14),--11 (0