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
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Chapter 6 Solutions
Numerical Analysis
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