The second-order Adams-Bashforth method for the integration of a single first-order differential equation d.x =f(t, x) dt is Xn+1 = X₁ + 1 h[3f(t, Xn) – f(tn-1, Xn-1)] Write down the appropriate equations for applying the same method to the solution of the pair of differential equations dx == f₁(t, x, y), dy= dy = f(t, x, y) dt dt Hence find the value of X(0.3) for the initial-value problem d²x dx + x = sint, x(0) = 0, dx (0) = 1 dt² dt dt using this Adams-Bashforth method with step size h = 0.1. Use the second-order predictor-corrector method for the first step to start the computation.
The second-order Adams-Bashforth method for the integration of a single first-order differential equation d.x =f(t, x) dt is Xn+1 = X₁ + 1 h[3f(t, Xn) – f(tn-1, Xn-1)] Write down the appropriate equations for applying the same method to the solution of the pair of differential equations dx == f₁(t, x, y), dy= dy = f(t, x, y) dt dt Hence find the value of X(0.3) for the initial-value problem d²x dx + x = sint, x(0) = 0, dx (0) = 1 dt² dt dt using this Adams-Bashforth method with step size h = 0.1. Use the second-order predictor-corrector method for the first step to start the computation.
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
100%
![2.4.3
The second-order Adams-Bashforth
method for
the integration of a single first-order differential
equation
dx
== f(t, x)
dt
is
Xn+1 = X₂ + 1 h[3f(tns Xn) − ƒ(tn-19 Xn-1)]
Write down the appropriate equations for applying
the same method to the solution of the pair of
differential equations
dx
= f₁(t, x, y), d=f₂(t, x, y)
dt
Hence find the value of X(0.3) for the initial-value
problem
d²x
2 dx
+x= sint, x(0)=0, dx (0) = 1
-
di²
dt
dt
using this Adams-Bashforth method with step size
h = 0.1. Use the second-order predictor-corrector
method for the first step to start the computation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8222824-b0b2-4366-bd51-0b90537c8121%2F3811fa39-0a51-45bb-b189-7dc6ce2c8c78%2F1im5e6r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.4.3
The second-order Adams-Bashforth
method for
the integration of a single first-order differential
equation
dx
== f(t, x)
dt
is
Xn+1 = X₂ + 1 h[3f(tns Xn) − ƒ(tn-19 Xn-1)]
Write down the appropriate equations for applying
the same method to the solution of the pair of
differential equations
dx
= f₁(t, x, y), d=f₂(t, x, y)
dt
Hence find the value of X(0.3) for the initial-value
problem
d²x
2 dx
+x= sint, x(0)=0, dx (0) = 1
-
di²
dt
dt
using this Adams-Bashforth method with step size
h = 0.1. Use the second-order predictor-corrector
method for the first step to start the computation.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
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,
