Euler's method is a numerical method for generating a table of values (xi, yi) that approximate the solution of the differential equation y' = f(x,y) with boundary condition y(xo) = yo. The first entry in the table is the starting point (xo , yo.). Given the entry (xi , yi ), then entry (xi+1 , yi+1) is obtained using the formula xi+1 = xi + x and yi+1 = yi + xf(xi , yi ). Where h is the small value called step size. Use Euler's method to estimate the value of y when x = 2.5 for the solution of the differential equation y' = x + 3y/x with the boundary condition y(1) = 1. Take x = 0.1, the exact solution of this differential equation is y = 2x3- x2. Compare your approximation values with the exact value
Euler's method is a numerical method for generating a table of values (xi, yi) that approximate the solution of the differential equation y' = f(x,y) with boundary condition y(xo) = yo. The first entry in the table is the starting point (xo , yo.). Given the entry (xi , yi ), then entry (xi+1 , yi+1) is obtained using the formula xi+1 = xi + x and yi+1 = yi + xf(xi , yi ). Where h is the small value called step size. Use Euler's method to estimate the value of y when x = 2.5 for the solution of the differential equation y' = x + 3y/x with the boundary condition y(1) = 1. Take x = 0.1, the exact solution of this differential equation is y = 2x3- x2. Compare your approximation values with the exact value
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Euler's method is a numerical method for generating a table of values (xi, yi) that approximate the
solution of the differential equation y' = f(x,y) with boundary condition y(xo) = yo. The first entry in the
table is the starting point (xo , yo.). Given the entry (xi , yi ), then entry (xi+1 , yi+1) is obtained using the
formula xi+1 = xi + x and yi+1 = yi + xf(xi , yi ). Where h is the small value called step size.
Use Euler's method to estimate the value of y when x = 2.5 for the solution of the differential equation
y' = x + 3y/x with the boundary condition y(1) = 1. Take x = 0.1, the exact solution of this differential
equation is y = 2x3- x2. Compare your approximation values with the exact value
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