The initial temperature of a long thin rod is u(x, 0) = 40, and the rod is divided into three equal segments as the following: node = 0 1 3 T=80°C T=20°C 9cm The temperature at node 1 (using Ax= 3cm and At = 0.1s) by using the explicit method is

Q: 2. Use Euler method to compute ys for the DE yy'=2x for y(1)=3

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Q: Use Euler's Method with h = 0.1 to approximate the solution to the following initial value problem…

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Q: 1. Given the initial values are xo =2 and x, =3, find the solution x3 for f(x)=x -6 by using %3D %3D…

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Q: 8. Consider the IVP y"" = t+y², y(0) = 1, y'(0) = 1, y"(0) = -1. Use Euler's method with step size h…

A: Given that :  IVPy"'=t+y2 ,y(0)=1,y"'(0)=1, y"(0)=1 h=.5  To Find : estimate the value of y(2)

Q: 1- Solve = cos x + y, where y = dy dx 2.0 at x 0 take step size h = Ax= 0.1 and solve for 0 ≤ x ≤…

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Q: Use Euler's Method with step size h=0.1 to approximate y(1.2), where y(x) satisfies the following…

A: Given initial value problem is  y'=3x+y y1=31

Q: Q1: Find y(0.5) for y'--2r-y, y(0) = -1, with step length (h= 0.1) using Euler method.

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Q: Given that y' = 2x + x²y, where y(0) = -1 with step size h=0.1. Estimate the values of y(0.2) using…

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A: dydx= f(x , y)dydx=1x2(y+3)The Euler method is given by : yn+1=yn+hf(xn,yn)Here f(x,y) =…

Q: 1) Approximate the value of y for 0sxs1.5 using the Euler method if the step length is h=0.5.

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Q: Apply Euler's method twice to approximate the solution to the initial value problem on the interval…

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Q: Given that y' = 2x2 – y + 3y2, where y = 0.5 at x = 2. Estimate the values of y(2.4) using the…

A: Let y'=f(x, y). Runge-kutta method of  fourth order also known as RK-4 method uses the formulas…

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Q: Let y'=3t and y(0)=0 Approximate y(4) using Euler's method with a step size of 2. Solve exactly…

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Q: Tank # 1 initially holds 50 gals of brine with a concentration of 1 lb/gal, while Tank # 2 initially…

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Q: Use Euler's method with step size 0.3 to compute the approximate y-values y(1.3) and y(1.6), of the…

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Q: by Use Euler's Method with h = 0.1 to approximate the solution to the following initial value…

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Q: Use Euler method to approximate the value of y(0.1), given               y' - x2 - y = 5 ,  y(0) =…

A: Euler Method:-  For a function fx, y the method is xi+1=xi+∆xyi+1=yi +h fxi, yi; i=0, 1, 2,... Here,…

Q: Consider the initial value problem у %3 х(у + х) — 2, y(0) = 2 Use Euler's method with step sizes h…

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Q: Consider the IVP: x" +3(x')2 + 10tx = 0, x(0) = - 3, x'(0) = 2 Using the Euler method with a time…

A: Given x''+3x'2+10tx=0, x0=-3, x'0=2, ∆t=0.5

Q: Apply Euler's method twice to approximate the solution to the initial value problem on the interval…

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Q: Use Euler's method with step size 0.1 to estimate y(0.4), where y() is the solution of the problem ₁…

A: Given: y'=x+y2 and step size h=0.1 with an initial value y0=0 To find: y0.4 in Euler's method and…

Q: Q4. Use Runge-Kutta Method of Order 4 to solve the following, using a step size of =0.1 for 0SKS1 dy…

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Q: Use Euler's method with step size 0.5 to compute the approximate y-values y1, Y2, Y3 and y4 of the…

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Q: Show that this function satisfies the initial conditions yp(to) =0 and y'(to) =0, so it is a…

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Q: 5. Use the finite difference method of order two with step size h = 0.25 to solve y" – xy' – xy = 0,…

A: A  finite set is a set that has a finite number of elements. Informally, a finite set is a set in…

Q: 1. 2xy'+ xy'+ (x² 3) y=O a) Show thet a regulor singulerity Xa>0 is point. 6) Use froteniaw method…

A: (a) Given equation, We know that,

Q: 4. Use the composite trapezoidal and Simpson's rule, each with step length h = 0.2, to estimate…

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Q: is uslng Newton-Raphson method with 10 iterations y = -x² + x + 0.75 y + 5xy = x Employ initial…

A: solve the system of equation using initial gusses of x=y=1.2  y=-x2+x+0.75   ⇒…

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A: The given equation xy'=y lnx can be rewritten as y'=y ln(x)x. Now for any function y'=f(x,y) given…

Q: Apply Euler's Method to find an approximate solution to w(1) if (0)%3D2. Use a step size of 0.5. w+2…

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Q: Use the backward Euler method with h = 0.1 y'(t) + 1000cos(y(t))-100t = 0 y(0) = -0.5   find y(2)

A: Given y'(t) + 1000cos(y(t))-100t = 0 y(0) = -0.5and h = 0.1

Q: A computer will be required for the problem. In this Problem, an initial value problem and its exact…

A: Solving the 1st question. Given:

Q: Use Euler's method to approximate y(1.0). Start with step size h= 0.1, and then use successively…

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Q: Consider IVP: y' = y² + t², y (0) = 1. Using Euler's method with time step h find y (2) . 0.5.

A: Euler's method yn+1=yn+h⋅f(tn,yn)where  tn+1=tn+h

Q: 2. Estimate the solution at z 3 for 2r-y y0) -1 using Euler's Method with a step size of h=1. (a) 1…

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Q: Use Euler method to approximate the value of y(0.1), given y' - 4y = 3x2, y(0) = 5 with Ax = 0.02

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Q: Use the Improved Euler method with step size 0.25 to y(x) estimate (1), where is the solution of the…

A: The given differential equation is y'=1-y-y3,  y0=0. To find: the value of y(1) by Improved Euler…

Q: Let y'=3t and y(0)=0 Approximate y(4) using Euler's method with step sizes of 1. Solve exactly and…

A: Given that, h=1t0=0y0=0ft,y=3t

Q: 1. Given an IVP y' = f(x,y), y(1) = y0, how many iterations of Euler’s method needs to be applied to…

A: The Eulers method states that: yn+1=yn+hfxn,yn The value of h=0.05, therefore to calculate the value…

Q: Use Runge-Kutta method of order four with step-size h = 0.25 to approximate the solution for 2 st<3…

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Q: In the initial value problem, use Euler's method with step sizes h=0.1, 0.02, 0.004, and 0.0008 to…

A: Given: A initial value problem, y'=x+4x, y0=5, 0≤x≤2 with steps size h=0.1, 0.02, 0.004, 0.0008. To…

Q: Apply Euler's method twice to approximate the solution to the initial value problem on the interval…

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Q: Use Euler's method with step size 0.250.25 to compute the approximate yy-values y1,y1, y2,y2, y3,y3,…

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Q: In the initial value problem, use Euler's method with step sizes h=0.1,0.02, 0.004, and 0.0008 to…

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