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Theory and Modern Applications

Table 1 Comparison of exact and numerical solutions for Example 4.1

From: Approximate solution of linear Volterra integro-differential equation by using cubic B-spline finite element method in the complex plane

x

exact solution

CBS-FEM

LBS-FEM

error(CBS-FEM)

error(LBS-FEM)

0.1

0.044664 − i0.098669

0.042820 − i0.098403

0.044050 − i0.098687

0.001863

0.000061

0.2

0.174664 − i0.189418

0.173427 − i0.188851

0.173440 − i0.189375

0.001361

0.001225

0.3

0.378390 − i0.264642

0.375337 − i0.263756

0.376476 − i0.264457

0.003179

0.001923

0.4

0.637642 − i0.317356

0.633653 − i0.316139

0.634900 − i0.316972

0.004171

0.002768

0.5

0.929263 − i0.341471

0.923961 − i0.340041

0.925567 − i0.340893

0.005491

0.003741

0.6

1.227202 − i0.332039

1.220711 − i0.330465

1.222553 − i0.331356

0.006679

0.004699

0.7

1.504846 − i0.285450

1.498093 − i0.284178

1.499533 − i0.284814

0.006872

0.005351

0.8

1.737394 − i0.199574

1.730275 − i0.198350

1.732179 − i0.199139

0.007223

0.005232

0.9

1.904072 − i0.073848

1.900770 − i0.073877

1.900372 − i0.073677

0.003302

0.003704