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(b- Employ the classical fourth-order Runge-Kutta (RK) method to integrate dy dt = y – t? + 1 from t=0 to 0.2 with a step size of 0.05. The initial condition at t=0 is y=0.5.

(b- Employ the classical fourth-order Runge-Kutta (RK) method to integrate dy dt = y – t? + 1 from t=0 to 0.2 with a step size of 0.05. The initial condition at t=0 is y=0.5.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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Employ the classical fourth-order Runge-Kutta (RK) method to integrate
??/?? = ? − ?^2 + 1
from t=0 to 0.2 with a step size of 0.05. The initial condition at t=0 is y=0.5

(b- Employ the classical fourth-order Runge-Kutta (RK) method to integrate dy = y – t² + 1 dt from t=0 to 0.2 with a step size of 0.05. The initial condition at t=0 is y=0.5.
Transcribed Image Text:(b- Employ the classical fourth-order Runge-Kutta (RK) method to integrate dy = y – t² + 1 dt from t=0 to 0.2 with a step size of 0.05. The initial condition at t=0 is y=0.5.
(c- Compare the true percent relative error values ( |&|%) Note that the exact ( analytical) solution was given in the tables. t Ytrue YEuler |&| (%) 0.0 0.50000 0.50000 0.05 0.57686 0.1 0.65741 0.15 0.74158 0.2 0.82929 t Ytrue YFourth-Order RK |&| (%) 0.0 0.50000 0.50000 --- 0.05 0.57686 0.1 0.65741 0.15 0.74158 0.2 0.82929
Transcribed Image Text:(c- Compare the true percent relative error values ( |&|%) Note that the exact ( analytical) solution was given in the tables. t Ytrue YEuler |&| (%) 0.0 0.50000 0.50000 0.05 0.57686 0.1 0.65741 0.15 0.74158 0.2 0.82929 t Ytrue YFourth-Order RK |&| (%) 0.0 0.50000 0.50000 --- 0.05 0.57686 0.1 0.65741 0.15 0.74158 0.2 0.82929
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