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Table 2 The absolute errors of the approximate and exact solutions for Example 2

From: Existence and approximation of solution for a nonlinear second-order three-point boundary value problem

x

\(\boldsymbol{\varphi_{m,n}(x)}\) : The present method

\(\boldsymbol{\varphi_{h}(x)}\) : The difference method

(2,1)

(2,2)

(4,1)

(4,2)

h  = 0.1

h  = 0.05

0.00

1.8390e − 3

9.9247e − 4

1.0502e − 3

1.6925e − 4

4.9821e − 2

2.5019e − 2

0.10

3.7770e − 3

1.2501e − 3

1.5834e − 3

2.2288e − 4

4.5369e − 2

2.2780e − 2

0.20

5.6959e − 3

1.5063e − 3

2.0998e − 3

2.7613e − 4

4.0870e − 2

2.0517e − 2

0.30

7.5115e − 3

1.7571e − 3

2.5446e − 3

3.2734e − 4

3.6285e − 2

1.8212e − 2

0.40

9.0093e − 3

1.9876e − 3

2.9475e − 3

3.7623e − 4

3.1581e − 2

1.5848e − 2

0.50

9.7699e − 3

2.1512e − 3

3.2074e − 3

4.1161e − 4

2.6730e − 2

1.3411e − 2

0.60

9.9119e − 3

2.2428e − 3

3.2926e − 3

4.2675e − 4

2.1712e − 2

1.0891e − 2

0.70

9.8280e − 3

2.3012e − 3

3.2046e − 3

4.2358e − 4

1.6516e − 2

8.2834e − 3

0.80

9.0100e − 3

2.2273e − 3

2.5986e − 3

3.3970e − 4

1.1146e − 2

5.5885e − 3

0.90

6.3775e − 3

1.7078e − 3

1.7315e − 3

2.2813e − 4

5.6224e − 3

2.8184e − 3