3. Solve the Laplace equation V²= 0 in 0 < x, y < 0.6 over a grid of mesh length 0.2.Given U = e¯* sin(y) on the boundary of the square region 0 < x, y < 0.6. Use Gauss-Seidel method with zero vector as an initial solution for three iterations.

Express differential equation to finite difference.

Answered: 3. Solve the Laplace equation V²= 0 in…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Use the backward Euler method with h = 0.1 y'(t) + 1000cos(y(t))-100t = 0 y(0) = -0.5 find y(2)
Q11) Let T₁ = 0, 7₂ = 3 be the roots of the indicial equation at x = 0 of the D.E. xy" - 2y + y = 0. If y₁ is the solution corresponding to r = 3, then a second linearly independent solution can be written as y2 = (A) y₁ ln x + Σn=1 anx-3 (B) cy₁ ln x +Enzo anan-3, c is constant (C) y₁ ln x +Σn=1 anx (D) cy₁ ln x +Enzo anx", c is constant (E) cy₁ lnx + Σn=0 anx+3, c is constant
4. Find the order of the given DE. Also, decide if the DE is linear or nonlinear. (a) + yx = x (b) 1 - y³ = 3x d'y - y3 = 3x I dx2 (c) y'- Iny = 0 (d) + 2 + = 2sin(x) d°y dx3 dx2
Given ( x''+2x'+2x=2delta(t-pi)....x(0)=0, x'(0)=0 Solve using LaplaceTransforms, show support work. Identify theforcing response in your solution.
a.) Form the complimentary solution to the homogeneous equation. y_c(t) = c_1 [ _ _] + c_2 [ _ _] b.) Construct a particular solution by assuming the form y_P(t) = e^(-3t)a and solving for the undetermined constant vector a. y_P(t) = [ _ _] c.) Form the general solution y(t) = y_c(t) + y_P(t) and impose the initial condition to obtain the solution of the initial value problem. [y_1(t) y_2(t)] = [ _ _]
Use the method of variation of parameters to produce a general solution of the inhomogenous equation y" + 2y' + y = x² +1
Find X, & X2 using Newton's method to minimize x2 – y?/2 starting from (1,1)
Consider the linear advection equation ut +a ux = 0. Discretise this equation by the finite difference method, using an explicit Euler discretisation for the aAt time derivative, and an upwind discretisation for the space derivative. At what value of the Courant number o = do we have a stable solution with Ax no dispersion and maximum diffusion errors? Give your answer to one decimal place.
Apply the improved Euler method to approximate the solution on the interval [0, 0.5] with step size h = 0.1. Construct a table showing values of the approximate solution and the actual solution at the points x = 0.1, 0.2, 0.3, 0.4, 0.5. y' y 3x-3, y(0) = 3; y(x) = 6+3x-3e* Complete the table below. (Round to four decimal places as needed.) ✗n Actual, y (xn) Improved Euler, yn 0.1 0.2 0.3 0.4 0.5
4. Solve the equation z' - V2(4– 4i) = 0, giving your answers in Cartesian form.
Verify by direct substitution that your general solution for (y₁, Y2) satisfies the Euler-Lagrange equations 4(zy, +₂) - zy₁" = 0 for y₁ ) & 2 (²y₁ + y₂) - 4 y₂²" = 0 > for y₂.
Consider the problem { ydu/dx-4xdu/dy=0 and U|c=x} where c={(x,-2x);x<0}. Discuss the local well-posedness of the problem. solve the problem by means of the method of characteristics

SEE MORE QUESTIONS

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

3. Solve the Laplace equation V²= 0 in 0 < x, y < 0.6 over a grid of mesh length 0.2. Given U =e* sin(y) on the boundary of the square region 0 < x, y < 0.6. Use Gauss- Seidel method with zero vector as an initial solution for three iterations.