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Theory and Modern Applications

Table 4 The maximum absolute error of the proposed method for different values of M and \(N=11\), \(n=4\), \(\alpha =1.95\) corresponding to Problem 4 at \(t=1\) and in [38]

From: On the approximation of time-fractional telegraph equations using localized kernel-based method

Our method

x

M = 15

M = 30

M = 40

M = 50

 

0

0

0

0

0

 

0.1

9.7426e−004

2.4335e−005

1.5203e−005

4.0419e−006

 

0.2

1.7345e−003

4.0736e−005

2.9554e−005

9.7154e−006

 

0.3

2.2774e−003

5.2554e−005

3.9710e−005

1.3668e−005

 

0.4

2.6032e−003

5.9667e−005

4.5773e−005

1.6012e−005

 

0.5

2.7118e−003

6.2035e−005

4.7793e−005

1.6794e−005

 

0.6

2.6032e−003

5.9666e−005

4.5773e−005

1.6012e−005

 

0.7

2.2774e−003

5.2553e−005

3.9711e−005

1.3669e−005

 

0.8

1.7345e−003

4.0737e−005

2.9553e−005

9.7145e−006

 

0.9

9.7426e−004

2.4337e−005

1.5201e−005

4.0403e−006

 

1

0

0

0

0

In [38]

x

m = 5

m = 7

m = 10

m = 15

 

0

0

0

0

0

 

0.1

1.6276e−003

1.6932e−004

2.9057e−004

6.8187e−005

 

0.2

2.4790e−003

1.0916e−003

3.7898e−004

8.7378e−005

 

0.3

2.3211e−003

1.0749e−003

3.8165e−004

8.8787e−005

 

0.4

2.1772e−003

1.0102e−003

3.6413e−004

8.4142e−005

 

0.5

2.1507e−003

9.9270e−004

3.5473e−004

8.2186e−005

 

0.6

2.1772e−003

1.0102e−003

3.6413e−004

8.4142e−005

 

0.7

2.3211e−003

1.0749e−003

3.8165e−004

8.8787e−005

 

0.8

2.4790e−003

1.0916e−003

3.7898e−004

8.7378e−005

 

0.9

1.6276e−003

1.6932e−004

2.9057e−004

6.8187e−005

 

1

0

0

0

0