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25.3 Use the (a) Euler and (b) Heun (without iteration) methods to solve d'y 2-1+y3D0 dt2 where y(0) = 2 and y'(0) = 0. Solve from x 0 to 4 using h = 0.1. %3D %3D

25.3 Use the (a) Euler and (b) Heun (without iteration) methods to solve d'y 2-1+y3D0 dt2 where y(0) = 2 and y'(0) = 0. Solve from x 0 to 4 using h = 0.1. %3D %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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25.3 Part (a) only

 

(e) Fourth-order RK method. 25.3 Use the (a) Euler and (b) Heun (without iteration) methods to ple 25.7. solve 25.15 Deve d²y -t+ y = 0 equations us duplicate the 25.16 The n di² is described where y(0) = 2 and y'(0) = 0. Solve from x 0 to 4 using h = 0.1. Compare the methods by plotting the solutions. 25.4 Solve the following problem with the fourth-order RK method: %3D %3D d²x dr d²y dy + 0.5 + 7y = 0 dx where x dis dx2 20-kg m damping coef (critically dam k= 20 N/m. TR m%3D where y(0) = 4 and y'(0) = 0. Solve from x = 0 to 5 with h = 0.5. %3D %3D %3D Plot your results. 25.5 Solve from t = 0 to 3 with h = 0.1 using (a) Heun (without %3D %3D corrector) and (b) Ralston's second-order RK method: x 1 m. Solv time period 0 S of the three val dy = y sin (t) dt y(0) = 1 FIGURE P25. dy =-y + y(0) = 1 dt Use the third-order RK method with a step size of 0.5.
Transcribed Image Text:(e) Fourth-order RK method. 25.3 Use the (a) Euler and (b) Heun (without iteration) methods to ple 25.7. solve 25.15 Deve d²y -t+ y = 0 equations us duplicate the 25.16 The n di² is described where y(0) = 2 and y'(0) = 0. Solve from x 0 to 4 using h = 0.1. Compare the methods by plotting the solutions. 25.4 Solve the following problem with the fourth-order RK method: %3D %3D d²x dr d²y dy + 0.5 + 7y = 0 dx where x dis dx2 20-kg m damping coef (critically dam k= 20 N/m. TR m%3D where y(0) = 4 and y'(0) = 0. Solve from x = 0 to 5 with h = 0.5. %3D %3D %3D Plot your results. 25.5 Solve from t = 0 to 3 with h = 0.1 using (a) Heun (without %3D %3D corrector) and (b) Ralston's second-order RK method: x 1 m. Solv time period 0 S of the three val dy = y sin (t) dt y(0) = 1 FIGURE P25. dy =-y + y(0) = 1 dt Use the third-order RK method with a step size of 0.5.
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