Skip to main content

Theory and Modern Applications

Table 3 Poincaré-type differential equation: Computation of \(u_{1}(t)\) for \(p=2\)

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

1.002

2

1.002

1.99533

0.002

1.00399

1.98668

1.00398

1.98206

0.003

1.00597

1.97346

1.00596

1.96888

0.004

1.00794

1.96033

1.00793

1.95579

0.005

1.00991

1.9473

1.00988

1.9428

0.006

1.01186

1.93436

1.01183

1.9299

0.007

1.0138

1.92151

1.01377

1.9171

0.008

1.01574

1.90875

1.0157

1.90438

0.009

1.01767

1.89608

1.01762

1.89175

0.01

1.01958

1.88351

1.01954

1.87921

0.1

1.15754

1.02648

1.15719

1.02459

1

0.891296

−0.844232

0.891478

−0.842916

3

0.110259

−1.09618

0.110554

−1.0952

4.99

0.0129359

−1.05457

0.0129902

−1.05395

4.991

0.0129222

−1.05455

0.0129765

−1.05394

4.992

0.0129086

−1.05453

0.0129628

−1.05392

4.993

0.012895

−1.05452

0.0129491

−1.0539

4.994

0.0128814

−1.0545

0.0129355

−1.05388

4.995

0.0128678

−1.05448

0.0129219

−1.05386

4.996

0.0128542

−1.05446

0.0129082

−1.05384

4.997

0.0128407

−1.05444

0.0128946

−1.05382

4.998

0.0128272

−1.05442

0.012881

−1.0538

4.999

0.0128136

−1.0544

0.0128675

−1.05378

5

0.0128001

−1.05438

0.0128539

−1.05376