Concept explainers
Apply the Adams-Bashforth Two-Step Method to the IVPs
with initial condition
a.
To find: the solution for the given IVPs problem for given step.
Explanation of Solution
Concept used:
Dr.Heun refer to an improved or modified Euler method (that is, an explicit trapezoidal rule)." from this it can be understood that the idea of an explicit trapezoidal rule is to replace the correct selection element on the right side with numerical approximation problems solution.
Calculation:
From this theorem known that using the Explicit Trapezoid Method with
For the remainder of the steps, we apply the Adams-Bash forth Two-Step Method, which is
Therefore
Global error at
b.
To find: the solution for the given IVPs problem for given step.
Explanation of Solution
Concept Used:
Dr.Heun refer to an improved or modified Euler method (that is, an explicit trapezoidal rule)." from this it can be understood that the idea of an explicit trapezoidal rule is to replace the correct selection element on the right side with numerical approximation problems solution.
Calculation:
From this theorem known that using the Explicit Trapezoid Method with
The Adams-Bash forth Two-Step Method is
Completing the last three steps results in the following table:
Global error at
c.
To find: the solution for the given IVPs problem for given step.
Explanation of Solution
Concept Used:
Dr.Heun refer to an improved or modified Euler method (that is, an explicit trapezoidal rule)." from this it can be understood that the idea of an explicit trapezoidal rule is to replace the correct selection element on the right side with numerical approximation problems solution.
Calculation:
From this theorem known that using the Explicit Trapezoid Method with
The Adams-Bash forth approximation
Global error at
d.
To find: the solution for the given IVPs problem for given step.
Explanation of Solution
Concept used:
Dr.Heun refer to an improved or modified Euler method (that is, an explicit trapezoidal rule)." from this it can be understood that the idea of an explicit trapezoidal rule is to replace the correct selection element on the right side with numerical approximation problems solution.
Calculation:
From this theorem known that using the Explicit Trapezoid Method with
The Adams-Bash forth approximation
Global error at
e.
To find: the solution for the given IVPs problem for given step.
Explanation of Solution
Concept used:
Dr.Heun refer to an improved or modified Euler method (that is, an explicit trapezoidal rule)." from this it can be understood that the idea of an explicit trapezoidal rule is to replace the correct selection element on the right side with numerical approximation problems solution.
Calculation:
From this theorem known that using the Explicit Trapezoid Method with
The Adams-Bash forth approximation
Global error at
f.
To find: the solution for the given IVPs problem for given step.
Explanation of Solution
Concept used:
Dr.Heun refer to an improved or modified Euler method (that is, an explicit trapezoidal rule)." from this it can be understood that the idea of an explicit trapezoidal rule is to replace the correct selection element on the right side with numerical approximation problems solution.
Calculation:
From this theorem known that using the Explicit Trapezoid Method with
The Adams-Bash forth approximation
Global error at
Want to see more full solutions like this?
Chapter 6 Solutions
Numerical Analysis, Books A La Carte Edition (3rd Edition)
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education