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

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