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Theory and Modern Applications

Table 6 Kneser’s differential equation: Computation of Sinus solution for \(\phi (t)=-\frac{2}{(t+1)^{2}}\)

From: Computation of solutions to linear difference and differential equations with a prescribed asymptotic behavior

t

\(u_{1}(t)\) exact

EE with \(u_{1}(T)=\sin (T)\)

Corrected EE

TR with \(u_{1}(T)=\sin (T)\)

Corrected TR

0

1

0.00676985

1.0014

1.00073

0.9999

0.001

1

0.00676982

1.0014

1.00073

0.999901

0.002

1

0.0067698

1.0014

1.00073

0.999902

0.003

1

0.00676978

1.0014

1.00074

0.999905

0.004

1.00001

0.00676978

1.0014

1.00074

0.999908

0.005

1.00001

0.00676977

1.00141

1.00074

0.999913

0.006

1.00002

0.00676978

1.00141

1.00075

0.999919

0.007

1.00002

0.00676979

1.00142

1.00075

0.999925

0.008

1.00003

0.00676981

1.00142

1.00076

0.999933

0.009

1.00004

0.00676983

1.00143

1.00077

0.999941

0.01

1.00005

0.00676987

1.00144

1.00078

0.99995

0.05

1.00117

0.0067762

1.00251

1.00187

1.00107

0.1

1.00438

0.00679644

1.00567

1.00505

1.00429

0.15

1.00924

0.00682785

1.01048

1.00987

1.00915

0.2

1.01539

0.00686808

1.0166

1.01599

1.01531

0.25

1.02253

0.00691504

1.02371

1.0231

1.02246