Euler's method for a first order IVP y = f(x, y). (x)=b is the the following algorithm, From (xo-yo) we define a sequence of approximations to the solution of the differential equation so that at the nth stage, we have X = X-1 +h, y₁=Ya-1 +h-f(x-1 Yn-1). In this exercise we consider the IVP y = 1+ y² with y(-0.2) = 1. This equation is first order with exact solution y=tan(x + tan-¹(1)). Use Euler's method with h = 0.1 to approximate the solution of the differential equation. For this example we include the slope field to give a rough idea what the shape of the solution should look like. Apply Euler's method to complete the following table: In the first two rows enter the values of x, and y, and in the third row use the exact solution to find the errors e, ly(x)-yal. A calculator or other scientific software would be handy to work these types of problem. You can always use answers given by explicit formulas which are very accurate. You need at least 4 significant digits. If your answer is marked wrong try entering a more accurate answer. 0 X₂ -0.2 Y₁ en 1 0 2
Euler's method for a first order IVP y = f(x, y). (x)=b is the the following algorithm, From (xo-yo) we define a sequence of approximations to the solution of the differential equation so that at the nth stage, we have X = X-1 +h, y₁=Ya-1 +h-f(x-1 Yn-1). In this exercise we consider the IVP y = 1+ y² with y(-0.2) = 1. This equation is first order with exact solution y=tan(x + tan-¹(1)). Use Euler's method with h = 0.1 to approximate the solution of the differential equation. For this example we include the slope field to give a rough idea what the shape of the solution should look like. Apply Euler's method to complete the following table: In the first two rows enter the values of x, and y, and in the third row use the exact solution to find the errors e, ly(x)-yal. A calculator or other scientific software would be handy to work these types of problem. You can always use answers given by explicit formulas which are very accurate. You need at least 4 significant digits. If your answer is marked wrong try entering a more accurate answer. 0 X₂ -0.2 Y₁ en 1 0 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
Plz don't use chat gpt.
Transcribed Image Text:Euler's method for a first order IVP y = f(x, y). (x)=b is the the following algorithm. From (xo. 3o) we define a sequence of approximations to
the solution of the differential equation so that at the nth stage, we have
X = Xa-1 +h, Y₁ = Ya-1 +h+ f(x-1 Yn-1).
In this exercise we consider the IVP y = 1+ y² with y(-0.2) = 1. This equation is first order with exact solution y = tan(x + tan-¹(1)).
Use Euler's method with h = 0.1 to approximate the solution of the differential equation.
For this example we include the slope field to give a rough idea what the shape of the solution should look like.
Apply Euler's method to complete the following table:
In the first two rows enter the values of x, and y, and in the third row use the exact solution to find the errors e, ly(x)-y.l. A calculator or other
scientific software would be handy to work these types of problem. You can always use answers given by explicit formulas which are very accurate. You
need at least 4 significant digits. If your answer is marked wrong try entering a more accurate answer.
P 0
X -0.2
y 1
e
0
2
3
4
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 32 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
