Differential Equations by Krantz Steven;

Author:Krantz, Steven;
Language: eng
Format: epub
Publisher: CRC Press LLC
Published: 2020-08-15T00:00:00+00:00

and use the value y(1) as a benchmark.

EXAMPLE 5.4.1 Apply the improved Euler method to the differential equation

(5.4.1.1)

with step size 0.2 and gauge the improvement in accuracy over the ordinary Euler method used in Examples 5.2.1 and 5.3.2.

■

TABLE 5.4.1.2. Tabulated values for exact and numerical solutions to (5.4.1.1) with h = 0.2 using the improved Euler method xn

yn

Exact

0.0

1.00000

1.00000

0.00

0.2

1.24000

1.24281

0.23

0.4

1.57680

1.581.12.25

0.43

0.6

2.03170

2.04424

0.61

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