Publications

2011
  • Ghinelli, Dina; Key, Jennifer D. Codes from incidence matrices and line graphs of Paley graphs. Adv. Math. Commun. 5 (2011), no. 1, 93–108, 94B05 (05C50 05C62)

  • Bashier, Eihab B. M.; Patidar, Kailash C.: A fitted numerical method for a system of partial delay differential equations. Comput. Math. Appl. 61 (2011), no. 6, 1475–1492, 65M06 (35K51 35R10 65M12 65M20)

  • Eihab B. M. Bashier, Kailash C. Patidar: A novel fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation. Applied Mathematics and Computation 217(9): 4728-4739.

  • Makasu, Cloud: Asymptotic behaviour of a nonlinear equation and its application. Commun. Nonlinear Sci. Numer. Simul. 16 (2011), no. 2, 610–612, 60G40 (34D05)

  • Hardie, K. A.; Kamps, K. H.; Witbooi, P. J. A coherent homotopy category of 2-track commutative cubes. Appl. Categ. Structures 19 (2011), no. 1, 39–60, 18D05 (18B30 55P10)

 

2010
  • Omar, M. R. The Lie algebra of a hyperbolic higher degree alternating form. Comm. Algebra 38 (2010), no. 4, 1351–1362. (Reviewer: Denis Ibadula), 11E76 (05E10 15A69 17B99)

  • Makasu, Cloud A note on explicit bounds for a stopped Feynman-Kac functional. Statist. Probab. Lett. 80 (2010), no. 23-24, 1977–1979, 60G40 (60J65)

  • Makasu, Cloud Controlling a stopped diffusion process to reach a goal. Statist. Probab. Lett. 80 (2010), no. 15-16, 1218–1222, 49K45 (60J65)

  • Key, J. D.; McDonough, T. P.; Mavron, V. C. Reed-Muller codes and permutation decoding. Discrete Math. 310 (2010), no. 22, 3114–3119. (Reviewer: Ángel del Río), 94B35 (94B05)

  • Key, J. D.; Rodrigues, B. G. Codes from lattice and related graphs, and permutation decoding. Discrete Appl. Math. 158 (2010), no. 16, 1807–1815. (Reviewer: Jon-Lark Kim), 94B05 (05C62 05C75 06C99)

  • Key, J. D.; Moori, J.; Rodrigues, B. G. Codes associated with triangular graphs and permutation decoding. Int. J. Inf. Coding Theory 1 (2010), no. 3, 334–349, 94B35 (05C75)

  • Fish, W.; Fray, R.; Mwambene, E.: Binary codes from the complements of the triangular graphs. Quaest. Math. 33 (2010), no. 4, 399–408, 94B05 (05B30 05C75 05E15)

  • Fish, W.; Key, J. D.; Mwambene, E. Codes from incidence matrices and line graphs of Hamming graphs. Discrete Math. 310 (2010), no. 13-14, 1884–1897, 94Bxx (05C76)

  • Fish, W.; Key, J. D.; Mwambene, Fish, W.; Key, J. D.; Mwambene, E. Binary codes from the line graph of the n-cube. J. Symbolic Comput. 45 (2010), no. 7, 800–812. (Reviewer: Keith E. Mellinger), 94B60 (05C90 94B05) Discrete Math. 310 (2010), no. 13-14, 1884–1897, 94Bxx (05C76)

  • Patidar, Kailash C. A new class of fitted mesh finite element method for convection-diffusion- reaction problems. Neural Parallel Sci. Comput. 18 (2010), no. 2, 237–252. (Reviewer: Nicolae Pop), 65L11 (65L10 65L60)

  • Kadalbajoo, Mohan K.; Patidar, Kailash C. Variable mesh spline approximation method for solving singularly perturbed turning point problems having interior layer. Neural Parallel Sci. Comput. 18 (2010), no. 2, 207–220. (Reviewer: Iuliu Sorin Pop), 65L11 (65L60)

  • Bashier, Eihab B. M.; Patidar, Kailash C. An almost second order fitted mesh numerical method for a singularly perturbed delay parabolic partial differential equation. Neural Parallel Sci. Comput. 18 (2010), no. 2, 137–154. (Reviewer: Rodney Josué Biezuner), 65M06 (35B25 35K20 35R10 65M50)

  • Munyakazi, Justin B.; Patidar, Kailash C. Higher order numerical methods for singularly perturbed elliptic problems. Neural Parallel Sci. Comput. 18 (2010), no. 1, 75–88. (Reviewer: Allaberen Ashyralyev), 65N06 (35B25 65N12)

  • Munyakazi, Justin B.; Patidar, Kailash C. Limitations of Richardson's extrapolation for a high order fitted mesh method for self-adjoint singularly perturbed problems. J. Appl. Math. Comput. 32 (2010), no. 1, 219–236. (Reviewer: S. Hitotumatu), 65B05 (65L11 65L12 65L20)

  • Makasu, Cloud A note on explicit bounds for a stopped Feynman-Kac functional. Statist. Probab. Lett. 80 (2010), no. 23-24, 1977–1979, 60G40 (60J65)

  • Makasu, Cloud Controlling a stopped diffusion process to reach a goal. Statist. Probab. Lett. 80 (2010), no. 15-16, 1218–1222, 49K45 (60J65)

 

2009
  • Fish, W.; Key, J. D.; Mwambene, E. Graphs, designs and codes related to the n-cube. Discrete Math. 309, no. 10, 3255–3269. (Reviewer: Man Keung Siu), 05B05 (05C50 05C51 94B35)

  • Makasu, Cloud A note on FBSDE characterization of mean exit times. C. R. Math. Acad. Sci. Paris 347 (2009), no. 15-16, 965–969, 60H10

  • Key, J. D.; Moori, J.; Rodrigues, B. G. Ternary codes from graphs on triples. Discrete Math. 309 (2009), no. 14, 4663–4681. (Reviewer: Paul Dorbec), 94B25 (05C50)

  • Makasu, Cloud Exit probability for an integrated geometric Brownian motion. Statist. Probab. Lett. 79 (2009), no. 11, 1363–1365, 60J65

  • Makasu, Cloud Bounds for a constrained optimal stopping problem. Optim. Lett. 3 (2009), no. 4, 499–505, 60G40

  • Witbooi, Peter J. On the localization genus of a direct product of metacyclic groups. J. Group Theory 12 (2009), no. 6, 845–857. (Reviewer: Valerij G. Bardakov), 20F18

  • Hardie, K. A.; Witbooi, P. J. Finite relational structure models of topological spaces and maps. Theoret. Comput. Sci. 405 (2008), no. 1-2, 24–34. (Reviewer: Luciano Stramaccia), 18B30 (03C65 54B30)

  • Key, J. D.; Moori, J.; Rodrigues, B. G. Partial permutation decoding of some binary codes from graphs on triples. Ars Combin. 91 (2009), 363–371, 05C50

  • Makasu, Cloud Stopping game on two stocks driven by Lévy processes. Sci. Math. Jpn. 69 (2009), no. 1, 27–33. (Reviewer: Erik J. Baurdoux), 60G40 (60G51 91A15 91A60)

  • Key, J. D.; McDonough, T. P.; Mavron, V. C. An upper bound for the minimum weight of the dual codes of Desarguesian planes. European J. Combin. 30 (2009), no. 1, 220–229. (Reviewer: Tsonka S. Baicheva), 51E22 (94B05)

  • Witbooi, P. J. Relative homotopy in relational structures. Canad. Math. Bull. 51 (2008), no. 2, 310–320. (Reviewer: Jie Wu), 55Q05 (06A07 18B30 54B30 55U05 55U35)

  • Witbooi, P. J. Relative homotopy in relational structures. Canad. Math. Bull. 51 (2008), no. 2, 310–320. (Reviewer: Jie Wu), 55Q05 (06A07 18B30 54B30 55U05 55U35)

 

2008
  • Patidar, Kailash C. A robust fitted operator finite difference method for a two-parameter singular perturbation problem. J. Difference Equ. Appl. 14 (2008), no. 12, 1197–1214, 65L12 (34E15 35B25 65L11)

  • Abelman, Shirley; Patidar, Kailash C. Comparison of some recent numerical methods for initial-value problems for stiff ordinary differential equations. Comput. Math. Appl. 55 (2008), no. 4, 733–744. (Reviewer: Neide Bertoldi Franco), 65L05

  • Munyakazi, Justin B.; Patidar, Kailash C. On Richardson extrapolation for fitted operator finite difference methods. Appl. Math. Comput. 201 (2008), no. 1-2, 465–480, 65L12

  • Makasu, Cloud On mean exit time from a curvilinear domain. Statist. Probab. Lett. 78 (2008), no. 17, 2859–2863, 60J60

  • Hardie, K. A.; Witbooi, P. J. Crown multiplications and a higher order Hopf construction. Topology Appl. 154 (2007), no. 10, 2073–2080. (Reviewer: A. R. Shastri), 55Q20 (06A11 55Q40)

  • Le Roux, Christiaan; Patidar, Kailash C. On the flow of a generalized Burgers fluid in an orthogonal rheometer. Nonlinear Anal. Real World Appl. 9 (2008), no. 5, 1882–1893, 35Q53 (76A10 76D05)

  • Makasu, Cloud On Wald optimal stopping problem for geometric Brownian motions. Sequential Anal. 27 (2008), no. 4, 435–440, 60G40 (60J65 62L15)

  • Makasu, Cloud On a problem of optimal stopping in mathematical finance. J. Interdiscip. Math. 11 (2008), no. 4, 581–591, 60G40 (60G51 91B28)

  • Makasu, Cloud On a decomposition result in a Dynkin stopping game. J. Inf. Optim. Sci. 29 (2008), no. 3, 523–530. (Reviewer: Krzysztof Szajowski), 91A15 (60G40 91A05 91A60 93E20)

  • Key, J. D.; Seneviratne, P. Permutation decoding for binary codes from lattice graphs. Discrete Math. 308 (2008), no. 13, 2862–2867. (Reviewer: Simon N. Litsyn), 94B35 (05C50 05E30 94B25)

  • Key, J. D.; McDonough, T. P.; Mavron, V. C. Partial permutation decoding for codes from affine geometry designs. J. Geom. 88 (2008), no. 1-2, 101–109. (Reviewer: Harold N. Ward), 94B25 (05B25 51E22)

  • Key, J. D.; Moori, J. Correction to: "Codes, designs and graphs from the Janko groups J1 and J2 '' [J. Combin. Math. Combin. Comput. 40 (2002), 143--159; MR1887973]. J. Combin. Math. Combin. Comput. 64 (2008), 153, 05B05 (05C25)

  • Key, Jennifer D.; Ngwane, Fidele F. A lower bound for the minimum weight of the dual 7-ary code of a projective plane of order 49. Des. Codes Cryptogr. 44 (2007), no. 1-3, 133–142, 94B05 (51E22)

 

2007
  • Hardie, K. A.; Witbooi, P. J. The Whitehead square of the 6-point 2-sphere. Quaest. Math. 29 (2006), no. 1, 1–7. (Reviewer: Alberto Cavicchioli), 55Q15 (55Q35)

  • Key, J. D.; Seneviratne, P. Permutation decoding for binary self-dual codes from the graph Qn where n is even. Advances in coding theory and cryptography, 152–159, Ser. Coding Theory Cryptol., 3, World Sci. Publ., Hackensack, NJ, 2007. (Reviewer: Jon-Lark Kim), 94B35 (94B25)

  • Key, J. D.; Seneviratne, P. Codes from the line graphs of complete multipartite graphs and PD- sets. Discrete Math. 307 (2007), no. 17-18, 2217–2225, 51E22 (05C90 94B05)

  • Key, J. D.; Seneviratne, P. Binary codes from rectangular lattice graphs and permutation decoding. European J. Combin. 28 (2007), no. 1, 121–126. (Reviewer: Ying Miao), 94B05 (51E22)

  • Patidar, Kailash C.; Shikongo, Albert The application of asymptotic analysis for developing reliable numerical method for a model singular perturbation problem. JNAIAM J. Numer. Anal. Ind. Appl. Math. 2 (2007), no. 3-4, 193–207. (Reviewer: Antoine Delcroix), 34E10 (34E15 65L10 65L12)

  • Lubuma, Jean M.-S.; Patidar, Kailash C. ε-uniform non-standard finite difference methods for singularly perturbed nonlinear boundary value problems. Adv. Math. Sci. Appl. 17 (2007), no. 2, 651–665. (Reviewer: J. Vigo- Aguiar), 65L12 (65L10)

  • Lubuma, Jean M.-S.; Patidar, Kailash C. Solving singularly perturbed advection-reaction equations via non-standard finite difference methods. Math. Methods Appl. Sci. 30 (2007), no. 14, 1627–1637, 35L60 (35B2565M06)

  • Patidar, Kailash C. High order parameter uniform numerical method for singular perturbation problems. Appl. Math. Comput. 188 (2007), no. 1, 720–733, 65L10

  • Lubuma, Jean M.-S.; Patidar, Kailash C. Non-standard methods for singularly perturbed problems possessing oscillatory/layer solutions. Appl. Math. Comput. 187 (2007), no. 2, 1147–1160, 34E15 (65L10)

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    2006
  • Fransman, Andrew; Witbooi, Peter Direct cancellation of finite groups. Algebra Colloq. 12 (2005), no. 4, 563–566, 20D99

  • Kadalbajoo, Mohan K.; Patidar, Kailash C.; Sharma, Kapil K. ε-uniformly convergent fitted methods for the numerical solution of the problems arising from singularly perturbed general DDEs. Appl. Math. Comput. 182 (2006), no. 1, 119–139, 65L12 (34K26 34K28)

  • Key, J. D. Recent developments in permutation decoding. Not. S. Afr. Math. Soc. 37 (2006), no. 1, 2–13, 94B25 (05A05 94-02)

  • Key, J. D.; Moori, J.; Rodrigues, B. G. Binary codes from graphs on triples and permutation decoding. Ars Combin. 79 (2006), 11–19, 94B35 (05A05 05C50 94B25)

  • Key, J. D.; McDonough, T. P.; Mavron, V. C. Information sets and partial permutation decoding for codes from finite geometries. Finite Fields Appl. 12 (2006), no. 2, 232–247. (Reviewer: Sapna Jain), 94B35 (94B25)

  • Key, J. D.; Moori, J.; Rodrigues, B. G. Some binary codes from symplectic geometry of odd characteristic. Util. Math. 67 (2005), 121–128. (Reviewer: Jonathan I. Hall), 94B05 (51E22)

  • Kadalbajoo, Mohan K.; Patidar, Kailash C. ε-uniformly convergent fitted mesh finite difference methods for general singular perturbation problems. Appl. Math. Comput. 179 (2006), no. 1, 248–266, 65L12 (65L10)

  • Patidar, Kailash C.; Sharma, Kapil K. Uniformly convergent non-standard finite difference methods for singularly perturbed differential-difference equations with delay and advance. Internat. J. Numer. Methods Engrg. 66 (2006), no. 2, 272–296. (Reviewer: Natesan Srinivasan), 65L10 (65L12)

  • Lubuma, Jean M.-S.; Patidar, Kailash C. Uniformly convergent non-standard finite difference methods for self-adjoint singular perturbation problems. J. Comput. Appl. Math. 191 (2006), no. 2, 228–238, 65L12 (65L10)

  • Patidar, Kailash C.; Sharma, Kapil K. ε-uniformly convergent non-standard finite difference methods for singularly perturbed differential difference equations with small delay. Appl. Math. Comput. 175 (2006), no. 1, 864–890