Example. Solve the following nonlinear Goursat problem thay = exter u(x, 0) = In(2)- 2 In(1 + e*), u(0, y) = In(2)- 2 In(1 + e³), u(0,0) = -In(2). Example. Solve the following Burgers equation u₁+uux = Uxx, u(x, 0) = x Example. Use the Adomian decomposition method to solve the following nonlinear Schrodinger equation iu, +uxx+2|u|2u= 0, u(x, 0) = ex Example. Solve the following homogeneous KdV equation: Ut 6uux + xxx = 0, u(x, 0) = 6x Example. Solve the fourth order differential equation: x u(x,t) ax4 = 0, u(x, 0) = 0, u(x, 0) = 1 + 120 3³u(x, t) + (+120) atz Example. We consider the system of PDEs: i. U₁ + vx = 0 V₁₂+ux = 0 with the initial data u(x, 0) = ex v(x, 0) = ex ii. U₁+ux + 2v = 0 V+Vx-2u= 0 with the initial data u(x, 0) = cos(x) v(x, 0) = sin(x) Solving by Adomian?
Example. Solve the following nonlinear Goursat problem thay = exter u(x, 0) = In(2)- 2 In(1 + e*), u(0, y) = In(2)- 2 In(1 + e³), u(0,0) = -In(2). Example. Solve the following Burgers equation u₁+uux = Uxx, u(x, 0) = x Example. Use the Adomian decomposition method to solve the following nonlinear Schrodinger equation iu, +uxx+2|u|2u= 0, u(x, 0) = ex Example. Solve the following homogeneous KdV equation: Ut 6uux + xxx = 0, u(x, 0) = 6x Example. Solve the fourth order differential equation: x u(x,t) ax4 = 0, u(x, 0) = 0, u(x, 0) = 1 + 120 3³u(x, t) + (+120) atz Example. We consider the system of PDEs: i. U₁ + vx = 0 V₁₂+ux = 0 with the initial data u(x, 0) = ex v(x, 0) = ex ii. U₁+ux + 2v = 0 V+Vx-2u= 0 with the initial data u(x, 0) = cos(x) v(x, 0) = sin(x) Solving by Adomian?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Example. Solve the following nonlinear Goursat problem
thay = exter
u(x, 0) = In(2)- 2 In(1 + e*),
u(0, y) = In(2)- 2 In(1 + e³),
u(0,0) = -In(2).
Example. Solve the following Burgers equation
u₁+uux = Uxx,
u(x, 0) = x
Example. Use the Adomian decomposition method to solve the following nonlinear
Schrodinger equation
iu, +uxx+2|u|2u= 0, u(x, 0) = ex
Example. Solve the following homogeneous KdV equation:
Ut
6uux + xxx = 0,
u(x, 0) = 6x
Example. Solve the fourth order differential equation:
x
u(x,t)
ax4
= 0, u(x, 0) = 0, u(x, 0) = 1 +
120
3³u(x, t) + (+120)
atz
Example. We consider the system of PDEs:
i.
U₁ + vx = 0
V₁₂+ux = 0
with the initial data
u(x, 0) = ex
v(x, 0) = ex
ii.
U₁+ux + 2v = 0
V+Vx-2u= 0
with the initial data
u(x, 0) = cos(x)
v(x, 0) = sin(x)
Solving by Adomian?
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