1a as t increasesOn the other hand, in Example 3 the general solution of theyProblemsNote about Variations of Computed Results. Most of the problemsin this section call for fairly extensive numerical computations. Tohandle these problems you need suitable computing hardware andsoftware. Keep in mind that numerical results may vary somewhat,depending on how your program is constructed and on how yourmputer executes arithmetic steps, rounds off, and so forth. Minorvariations in the last decimal place may be due to such causes and donot necessarily indicate that something is amiss. Answers in the back7 1++ ce²t,+ ceis a diverging family. Note that solutions corresponding to two nearby values of c becomeand, because the term involving the arbitrary constant c grows without bound as t → ∞, thisapart as t increases. In Example 3 we are trying approximate the solution forarbitrarily farc = 11/4, but in the use of Euler's method we areactually at each step following anothersolution thatthe errors in Example 3 are so much larger than those in Example 2.I separates from the desired one faster and faster as t increases. This explains whyIn using a numerical procedure such as the Euler method, you must always keep in mindthe accuracy of the numerical results could be determined directly by a comparison with thethe question of whether the results are accurate enough to be useful. In the preceding examples,solution obtained analytically. Of course, usually the analytical solution is not available if anumerical procedure is to be employed, so what we usually need are bounds for, or at leastestimates of, the error that do not require a knowledge of the exact solution. You should alsokeep in mind that the best that we can expect, or hope for, from a numerical approximationis that it reflects the behavior of the actual solution. Thus a member of a diverging family ofsolutions will always be harder to approximate than a member of a converging family.If you wish to read more about numerical approximations to solutions of initial valueproblems, you may go directly to Chapter 8 at this point. There, we present some informationon the analysis of errors and also discuss several algorithms that are computationally muchmore efficient than the Euler method.(18)15dmomof the book are recorded to six digits in most cases, although moredigits were retained in the intermediate calculations.In each of Problems 1 through 4:200Na. Find approximate values of the solution of the given initialvalue problem at t = 0.1, 0.2, 0.3, and 0.4 using the Eulermethod with h = 0.1.N b. Repeat part (a) with h = 0.05. Compare the results withdayondithose found in a.- as t increasesOn the other hand, in Example 3 the general solution of theyProblemsNote about Variations of Computed Results. Most of the problemsin this section call for fairly extensive numerical computations. Tohandle these problems you need suitable computing hardware andsoftware. Keep in mind that numerical results may vary somewhat,depending on how your program is constructed and on how yourmputer executes arithmetic steps, rounds off, and so forth. Minorvariations in the last decimal place may be due to such causes and donot necessarily indicate that something is amiss. Answers in the back7 1++ ce²t,+ ceis a diverging family. Note that solutions corresponding to two nearby values of c becomeand, because the term involving the arbitrary constant c grows without bound as t → ∞, thisapart as t increases. In Example 3 we are trying approximate the solution forarbitrarily farc = 11/4, but in the use of Euler's method we areactually at each step following anothersolution thatthe errors in Example 3 are so much larger than those in Example 2.I separates from the desired one faster and faster as t increases. This explains whyIn using a numerical procedure such as the Euler method, you must always keep in mindthe accuracy of the numerical results could be determined directly by a comparison with thethe question of whether the results are accurate enough to be useful. In the preceding examples,solution obtained analytically. Of course, usually the analytical solution is not available if anumerical procedure is to be employed, so what we usually need are bounds for, or at leastestimates of, the error that do not require a knowledge of the exact solution. You should alsokeep in mind that the best that we can expect, or hope for, from a numerical approximationis that it reflects the behavior of the actual solution. Thus a member of a diverging family ofsolutions will always be harder to approximate than a member of a converging family.If you wish to read more about numerical approximations to solutions of initial valueproblems, you may go directly to Chapter 8 at this point. There, we present some informationon the analysis of errors and also discuss several algorithms that are computationally muchmore efficient than the Euler method.(18)15dmomof the book are recorded to six digits in most cases, although moredigits were retained in the intermediate calculations.In each of Problems 1 through 4:200Na. Find approximate values of the solution of the given initialvalue problem at t = 0.1, 0.2, 0.3, and 0.4 using the Eulermethod with h = 0.1.N b. Repeat part (a) with h = 0.05. Compare the results withdayondithose found in a.-

y'=3+t-y Initial condition y0=1 We have to approximate the initial value problem at t=0.1, 0.2, 0.3…

Answered: 1. y'= 3+t-y, y(0) = 1

1. y'= 3+t-y, y(0) = 1

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

Similar questions

503 1 X
75%1
20 35 60
Advanced Math Question
V 2000 1500 1000 500 X 5 10 15 20
Simplify.
Which one of the following expressions is the value of the cosine of the acute angle between the vectors u = (1,2, 3) and v = (1, –2,3)? 3 (A) 7V2 2 (B) 7 (C) 7/2 3 (D)
9 08 t
Sol 1 ten thousand thousands
Write the following in terms of i and simplify. V- 25 81
Evaluate. 15C1
Fana& In3 76