Q1/ What is the relationship between Laplace transform L[u(t)] = F(s) = est u(t)dt 0 and the following transform 00 -st [u(t)] = W(s, v) = e evu(t)dt Q2/ Use Adomian decomposition method to solve the following nonlinear partial differential equations: uxx + u² - u² = 0, with initial conditions u(0,y) = 0, ux(0, y) = cos(y). Q3/ Use DJM to solve the following nonlinear Schrodinger equation: iut +uxx+2lulu = 0, u(x, 0) = ex Q4/Use SAM to solve the following differential equation: a²u(x, y) u(x, y) + u(x,y) = 0, дх² ay² with initial conditions u(o, y) =y, ux (0,y) = y + coshy. ====artomain==== Q5/ Use Laplace homotopy perturbation method to solve the following nonlinear partial differential equation: a²u(x, y, t) at² a² = (uxx Uyy). дхду дхду (xy ux uy) - u, with the initial conditions u(x, y, 0) = ey, u(x, y, 0) = exy.
Q1/ What is the relationship between Laplace transform L[u(t)] = F(s) = est u(t)dt 0 and the following transform 00 -st [u(t)] = W(s, v) = e evu(t)dt Q2/ Use Adomian decomposition method to solve the following nonlinear partial differential equations: uxx + u² - u² = 0, with initial conditions u(0,y) = 0, ux(0, y) = cos(y). Q3/ Use DJM to solve the following nonlinear Schrodinger equation: iut +uxx+2lulu = 0, u(x, 0) = ex Q4/Use SAM to solve the following differential equation: a²u(x, y) u(x, y) + u(x,y) = 0, дх² ay² with initial conditions u(o, y) =y, ux (0,y) = y + coshy. ====artomain==== Q5/ Use Laplace homotopy perturbation method to solve the following nonlinear partial differential equation: a²u(x, y, t) at² a² = (uxx Uyy). дхду дхду (xy ux uy) - u, with the initial conditions u(x, y, 0) = ey, u(x, y, 0) = exy.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Q1/ What is the relationship between Laplace transform
L[u(t)] = F(s) = est u(t)dt
0
and the following transform
00 -st
[u(t)] = W(s, v) = e
evu(t)dt
Q2/ Use Adomian decomposition method to solve the following nonlinear
partial differential equations:
uxx + u² - u² = 0,
with initial conditions
u(0,y) = 0, ux(0, y) = cos(y).
Q3/ Use DJM to solve the following nonlinear Schrodinger equation:
iut +uxx+2lulu = 0,
u(x, 0) = ex
Q4/Use SAM to solve the following differential equation:
a²u(x, y) u(x, y)
+
u(x,y) = 0,
дх²
ay²
with initial conditions
u(o, y) =y, ux (0,y) = y + coshy.
====artomain====
Q5/ Use Laplace homotopy perturbation method to solve the following
nonlinear partial differential equation:
a²u(x, y, t)
at²
a²
=
(uxx Uyy).
дхду
дхду
(xy ux uy) - u,
with the initial conditions
u(x, y, 0) = ey, u(x, y, 0) = exy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F446d6298-ca39-4f42-8695-26a09101ed7e%2F7a3bf0ba-aadc-4c82-bc0a-9f3d63782a3a%2Fz2evp2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q1/ What is the relationship between Laplace transform
L[u(t)] = F(s) = est u(t)dt
0
and the following transform
00 -st
[u(t)] = W(s, v) = e
evu(t)dt
Q2/ Use Adomian decomposition method to solve the following nonlinear
partial differential equations:
uxx + u² - u² = 0,
with initial conditions
u(0,y) = 0, ux(0, y) = cos(y).
Q3/ Use DJM to solve the following nonlinear Schrodinger equation:
iut +uxx+2lulu = 0,
u(x, 0) = ex
Q4/Use SAM to solve the following differential equation:
a²u(x, y) u(x, y)
+
u(x,y) = 0,
дх²
ay²
with initial conditions
u(o, y) =y, ux (0,y) = y + coshy.
====artomain====
Q5/ Use Laplace homotopy perturbation method to solve the following
nonlinear partial differential equation:
a²u(x, y, t)
at²
a²
=
(uxx Uyy).
дхду
дхду
(xy ux uy) - u,
with the initial conditions
u(x, y, 0) = ey, u(x, y, 0) = exy.
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