Journal of Mathematics

Research Article

Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations

Table 1

Computed rate of convergence and maximum errors for Example 1.
Number of mesh points 3N
1632641282565121024
Finite difference method
2.8530e − 031.6423e − 038.6257e − 044.3424e − 042.1521e − 041.0694e − 045.4208e − 05
3.0817e − 031.8315e − 039.9232e − 045.1418e − 042.6100e − 041.3150e − 046.6324e − 05
3.1526e − 031.8900e − 031.0321e − 035.3860e − 042.7489e − 041.3887e − 046.9901e − 05
3.1750e − 031.9083e − 031.0446e − 035.4624e − 042.7922e − 041.4116e − 047.1008e − 05
3.1820e − 031.9141e − 031.0486e − 035.4864e − 042.8058e − 041.4188e − 047.1355e − 05
3.1842e − 031.9159e − 031.0498e − 035.4940e − 042.8101e − 041.4211e − 047.1465e − 05
3.1849e−031.9165e−031.0502e − 035.4965e − 042.8115e− 041.4218e − 047.1499e − 05
3.1851e − 031.9167e − 031.0503e − 035.4972e − 042.8119e − 041.4220e − 047.1510e − 05
3.1851e − 031.9167e − 031.0503e − 035.4972e − 042.8119e − 041.4220e − 047.1510e − 05
7.327520e − 018.6771e − 019.3412e − 019.6712e − 019.8357e − 019.9178e − 01—
Hybrid difference method
1.6679e − 026.7615e − 032.4201e − 038.5271e − 042.6786e − 047.8677e − 052.6259e − 05
1.6684e − 026.7758e − 032.4331e − 038.6109e − 042.7258e − 048.3394e − 052.5535e − 05
1.6684e − 026.7772e − 032.4344e−038.6194e − 042.7307e − 048.4126e − 052.6113e − 05
1.6684e − 026.7774e − 032.4345e−038.6202e − 042.7312e − 048.4200e − 052.6192e − 05
1.6684e − 026.7774e − 032.4345e − 038.6203e − 042.7312e − 048.4207e − 052.6200e − 05
1.6684e − 026.7774e − 032.4345e − 038.6203e − 042.7312e − 048.4208e − 052.6201e − 05
1.6684e − 026.7774e − 032.4345e − 038.6204e − 042.7312e − 048.4209e − 052.6200e − 05
1.6685e − 026.7774e − 032.4346e − 038.6201e − 042.7308e − 048.4224e − 052.6206e − 05
1.6685e − 026.7774e − 032.4346e − 038.6204e − 042.7312e − 048.4224e − 052.6259e − 05
1.2997e + 001.4770e + 001.4979e + 001.6581e + 001.6972e + 001.6814e + 00—