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Theory and Modern Applications

Table 2 Poincaré-type differential equation: Numerical calculation of the one-dimensional subspace defined by the subdominant solution

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

t

EE: \(u_{1}(t)\)

EE: \(\frac{u_{1}(t)-u_{1}(t-h)}{hu_{1}(t-h)}\)

TR: \(u_{1}(t)\)

TR: \(\frac{u_{1}(t)-u_{1}(t-h)}{hu_{1}(t-h)}\)

0

1

inf

1

inf

0.001

0.998403

−1.59697

0.998403

−1.59677

0.002

0.996808

−1.59737

0.996809

−1.59717

0.003

0.995216

−1.59776

0.995216

−1.59757

0.004

0.993625

−1.59816

0.993626

−1.59796

0.005

0.992037

−1.59856

0.992038

−1.59836

0.006

0.99045

−1.59896

0.990452

−1.59876

0.007

0.988866

−1.59935

0.988868

−1.59915

0.008

0.987284

−1.59975

0.987286

−1.59955

0.009

0.985705

−1.60015

0.985706

−1.59994

0.01

0.984127

−1.60054

0.984129

−1.60033

0.1

0.85065

−1.63506

0.850673

−1.6347

1

0.174041

−1.85137

0.174195

−1.84999

3

0.00370203

−1.96093

0.00371804

−1.95906

4.99

7.25945e−005

−1.98241

7.31878e−005

−1.98047

4.991

7.24506e−005

−1.98242

7.30429e−005

−1.98047

4.992

7.23069e−005

−1.98243

7.28982e−005

−1.98048

4.993

7.21636e−005

−1.98243

7.27538e−005

−1.98048

4.994

7.20205e−005

−1.98244

7.26097e−005

−1.98049

4.995

7.18778e−005

−1.98244

7.24659e−005

−1.9805

4.996

7.17353e−005

−1.98245

7.23224e−005

−1.9805

4.997

7.15931e−005

−1.98246

7.21792e−005

−1.98051

4.998

7.14511e−005

−1.98246

7.20362e−005

−1.98051

4.999

7.13095e−005

−1.98247

7.18936e−005

−1.98052

5

7.11681e−005

−1.98247

7.17512e−005

−1.98052