Fig.1.
![Comparison of AEs of CNPS and CPS with [6] of problem 3.1 at h=110](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/68432e85f788d76dad45bfe1/j_ama-2025-0021_fig_001.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20251208%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251208T232506Z&X-Amz-Expires=3600&X-Amz-Signature=b7f387ab342f20d9c098dcdd931a220b92f93c9fee76aafd9fa982c160b9aed3&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Fig. 2.
Fig.3.
![Comparison of AEs of CNPS and CPS with [6] of problem 3.2 at h=110](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/68432e85f788d76dad45bfe1/j_ama-2025-0021_fig_003.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20251208%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251208T232506Z&X-Amz-Expires=3600&X-Amz-Signature=f319613b12a27fe52a062b6f0f864d92acaf2890015766f9169da214953f07ed&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Fig. 4.
Fig.5.
![Comparison of AEs of CNPS and CPS with [6] of problem 3.3 at h=110](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/68432e85f788d76dad45bfe1/j_ama-2025-0021_fig_005.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20251208%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251208T232506Z&X-Amz-Expires=3600&X-Amz-Signature=ed7c022b745cf6d005d1f9e7cb2457bebbea6791af980a0a8c84ce294e77f7b0&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Fig. 6.
Comparison of accurate, CNPS along with CPS for problem 3_1 at h=15
| Accurate solution | CNPS solution | |error| on CNPS | CPS solution | |error| on CPS | |
|---|---|---|---|---|---|
| 0 | 1 | 1 | 0.00E-00 | 1 | 0.00E-00 |
| 0.2 | 0.818730753 | 0.817688874 | 1.04E-03 | 0.817618382 | 1.11E-03 |
| 0.4 | 0.670320046 | 0.668633087 | 1.69E-03 | 0.668558559 | 1.76E-03 |
| 0.6 | 0.548811636 | 0.547122919 | 1.69E-03 | 0.547064978 | 1.75E-03 |
| 0.8 | 0.449328964 | 0.448284237 | 1.04E-03 | 0.448246958 | 1.08E-03 |
| 1 | 0.367879441 | 0.367879441 | 0.00E-00 | 0.367879441 | 0.00E-00 |
Comparison of accurate, CNPS along with CPS for problem 3_3 at h=110
| Accurate solution | CNPS solution | |error| on CNPS | CPS solution | |error| on CPS | [6] | |
|---|---|---|---|---|---|---|
| 0 | 1 | 1 | 1 | 0.00E-00 | 0.00E-00 | 0.00E-00 |
| 0.1 | 1.105170918 | 1.105171098 | 1.105120542 | 5.04E-05 | 1.80E-07 | 3.82E-06 |
| 0.2 | 1.221402758 | 1.221403102 | 1.221310719 | 9.20E-05 | 3.43E-07 | 1.35E-05 |
| 0.3 | 1.349858808 | 1.349859281 | 1.349734356 | 1.24E-04 | 4.73E-07 | 2.64E-05 |
| 0.4 | 1.491824698 | 1.491825254 | 1.49167782 | 1.47E-04 | 5.56E-07 | 3.85E-05 |
| 0.5 | 1.648721271 | 1.648721853 | 1.648562907 | 1.58E-04 | 5.82E-07 | 4.64E-05 |
| 0.6 | 1.8221188 | 1.82211935 | 1.821961083 | 1.58E-04 | 5.50E-07 | 4.70E-05 |
| 0.7 | 2.013752707 | 2.01375317 | 2.01360923 | 1.43E-04 | 4.62E-07 | 3.94E-05 |
| 0.8 | 2.225540928 | 2.225541259 | 2.225427036 | 1.14E-04 | 3.31E-07 | 2.48E-05 |
| 0.9 | 2.459603111 | 2.459603282 | 2.45953623 | 6.69E-05 | 1.70E-07 | 8.50E-06 |
| 1 | 2.718281828 | 2.71828 | 2.71828 | 0.00E-00 | 0.00E-00 | 0.00E-00 |
Comparison of accurate, CNPS along with CPS for problem 3_2 at h=15
| Accurate solution | CNPS solution | |error| on CNPS | CPS solution | |error| on CPS | |
|---|---|---|---|---|---|
| 0 | 1 | 1 | 0.00E-00 | 1 | 0.00E-00 |
| 0.2 | 0.654984602 | 0.654548343 | 4.36E-04 | 0.653822489 | 1.16E-03 |
| 0.4 | 0.402192028 | 0.401485267 | 7.07E-04 | 0.400509549 | 1.68E-03 |
| 0.6 | 0.219524654 | 0.218816219 | 7.08E-04 | 0.217928602 | 1.60E-03 |
| 0.8 | 0.089865793 | 0.089426899 | 4.39E-04 | 0.088878968 | 9.87E-04 |
| 1 | 0 | 0 | 0.00E-00 | 0 | 0.00E-00 |
Comparison of accurate, CNPS along with CPS for problem 3_2 at h=110
| Accurate solution | CNPS solution | |error| on CNPS | CPS solution | |error| on CPS | [6] | |
|---|---|---|---|---|---|---|
| 0 | 1 | 1 | 0.00E-00 | 1 | 0.00E-00 | 0.00E-00 |
| 0.1 | 0.814353676 | 0.814349741 | 0.814016517 | 3.37E-04 | 3.94E-06 | 1.91E-05 |
| 0.2 | 0.654984602 | 0.654977145 | 0.654367593 | 6.17E-04 | 7.46E-06 | 6.81E-05 |
| 0.3 | 0.518572754 | 0.518562529 | 0.517747628 | 8.25E-04 | 1.02E-05 | 1.24E-04 |
| 0.4 | 0.402192028 | 0.402180054 | 0.401241892 | 9.50E-04 | 1.20E-05 | 1.64E-04 |
| 0.5 | 0.30326533 | 0.303252787 | 0.302279968 | 9.85E-04 | 1.25E-05 | 1.72E-04 |
| 0.6 | 0.219524654 | 0.219512766 | 0.218594693 | 9.30E-04 | 1.19E-05 | 1.46E-04 |
| 0.7 | 0.148975591 | 0.148965506 | 0.148186139 | 7.89E-04 | 1.01E-05 | 9.70E-05 |
| 0.8 | 0.089865793 | 0.089858479 | 0.089290229 | 5.76E-04 | 7.31E-06 | 4.49E-05 |
| 0.9 | 0.040656966 | 0.040653124 | 0.040351558 | 3.05E-04 | 3.84E-06 | 9.44E-06 |
| 1 | 0 | 0 | 0 | 0.00E-00 | 0.00E-00 | 0.00E-00 |
Comparison of accurate, CNPS along with CPS for problem 3_1 at h=110
| Accurate solution | CNPS solution | |error| on CNPS | CPS solution | |error| on CPS | [6] | |
|---|---|---|---|---|---|---|
| 0 | 1 | 1 | 0.00E-00 | 1 | 0.00E-00 | 0.00E-00 |
| 0.1 | 0.904837418 | 0.904837481 | 6.27E-08 | 0.904812814 | 2.46E-05 | 3.82E-06 |
| 0.2 | 0.818730753 | 0.818730875 | 1.22E-07 | 0.818688854 | 4.19E-05 | 1.36E-05 |
| 0.3 | 0.740818221 | 0.740818391 | 1.70E-07 | 0.740765438 | 5.28E-05 | 2.49E-05 |
| 0.4 | 0.670320046 | 0.670320248 | 2.02E-07 | 0.670262025 | 5.80E-05 | 3.31E-05 |
| 0.5 | 0.60653066 | 0.606530874 | 2.14E-07 | 0.606472401 | 5.83E-05 | 3.50E-05 |
| 0.6 | 0.548811636 | 0.548811841 | 2.05E-07 | 0.548757603 | 5.40E-05 | 3.01E-05 |
| 0.7 | 0.496585304 | 0.496585478 | 1.74E-07 | 0.496539521 | 4.58E-05 | 2.03E-05 |
| 0.8 | 0.449328964 | 0.44932909 | 1.26E-07 | 0.449295105 | 3.39E-05 | 9.57E-06 |
| 0.9 | 0.40656966 | 0.406569726 | 6.61E-08 | 0.406551127 | 1.85E-05 | 2.11E-06 |
| 1 | 0.367879441 | 0.367879441 | 0.00E-00 | 0.367879441 | 0.00E-00 | 0.00E-00 |
Comparison of accurate, CNPS along with CPS for problem 3_3 at h=15
| Accurate solution | CNPS solution | |error| on CNPS | CPS solution | |error| on CPS | [6] | |
|---|---|---|---|---|---|---|
| 0 | 1 | 1 | 0.00E-00 | 1 | 0.00E-00 | 0.00E-00 |
| 0.2 | 1.221402758 | 1.221403377 | 6.19E-07 | 1.22103274 | 3.70E-04 | 5.42E-05 |
| 0.4 | 1.491824698 | 1.491825707 | 1.01E-06 | 1.491234204 | 5.90E-04 | 1.53E-04 |
| 0.6 | 1.8221188 | 1.822119714 | 9.13E-07 | 1.821484771 | 6.34E-04 | 1.95E-04 |
| 0.8 | 2.225540928 | 2.225541357 | 4.28E-07 | 2.225083141 | 4.58E-04 | 1.04E-04 |
| 1 | 2.718281828 | 2.71828 | 0.00E-00 | 2.71828 | 0.00E-00 | 0.00E-00 |