This work is licensed under the Creative Commons Attribution 4.0 International License.
Cannon J.R., The One-Dimensional Heat Equation, Cambridge University Press, UK, 1984.CannonJ.R.The One-Dimensional Heat EquationCambridge University PressUK1984Search in Google Scholar
Dhawan S., Kumar S., A numerical solution of one dimensional heat equation using cubic B-spline basis functions, International Journal of Research and Reviews in Applied Sciences, 1, 71–77, 2009.DhawanS.KumarS.A numerical solution of one dimensional heat equation using cubic B-spline basis functionsInternational Journal of Research and Reviews in Applied Sciences171772009Search in Google Scholar
Çağlar H., Özer M., Çağlar N., The numerical solution of the one-dimensional heat equation by using third degree B-spline functions, Chaos Solitons and Fractals, 38(4), 1197–1201, 2008.ÇağlarH.ÖzerM.ÇağlarN.The numerical solution of the one-dimensional heat equation by using third degree B-spline functionsChaos Solitons and Fractals384119712012008Search in Google Scholar
Wazwaz A.M., Partial Differential Equations methods and Applications, Saint Xavier University Press, USA, 2002.WazwazA.M.Partial Differential Equations methods and ApplicationsSaint Xavier University PressUSA2002Search in Google Scholar
Kaskar N.F., Modified implicit method for solving one dimensional heat equation, International Journal of Engineering Research in Computer Science and Engineering, 8(9), 1–6, 2021.KaskarN.F.Modified implicit method for solving one dimensional heat equationInternational Journal of Engineering Research in Computer Science and Engineering89162021Search in Google Scholar
Suárez-Carreño F., Rosales-Romero L., Convergency and stability of explicit and implicit schemes in the simulation of the heat equation, Applied Sciences, 11(10), 4468, 2021.Suárez-CarreñoF.Rosales-RomeroL.Convergency and stability of explicit and implicit schemes in the simulation of the heat equationApplied Sciences111044682021Search in Google Scholar
Goh J., Majid A.A., Ismail A.I.M., Cubic b-spline collocation method for one-dimensional heat and advection-diffusion equations, Journal of Applied Mathematics, 2012(ID:458701), 1–8, 2012.GohJ.MajidA.A.IsmailA.I.M.Cubic b-spline collocation method for one-dimensional heat and advection-diffusion equationsJournal of Applied Mathematics2012(ID:458701)182012Search in Google Scholar
Lozanda-Cruz G., Rubio-Mercedes C.E., Rodrigues-Ribeiro J., Numerical solution of heat equation with singular robin boundary condition, Tendências em Matemática Aplicada e Computacional, 19(2), 209–220, 2018.Lozanda-CruzG.Rubio-MercedesC.E.Rodrigues-RibeiroJ.Numerical solution of heat equation with singular robin boundary conditionTendências em Matemática Aplicada e Computacional1922092202018Search in Google Scholar
Hooshmandasl M.R., Heydari M.H., Maalek Ghaini F.M., Numerical solution of the one-dimensional heat equation by using chebyshev wavelets method, Journal of Applied and Computational Mathematics, 1(6), 1–7, 2012.HooshmandaslM.R.HeydariM.H.Maalek GhainiF.M.Numerical solution of the one-dimensional heat equation by using chebyshev wavelets methodJournal of Applied and Computational Mathematics16172012Search in Google Scholar
Han F., Dai W., New higher-order compact finite difference schemes for 1D heat conduction equations, Applied Mathematical Modelling, 37(16–17), 7940–7952, 2013.HanF.DaiW.New higher-order compact finite difference schemes for 1D heat conduction equationsApplied Mathematical Modelling3716–17794079522013Search in Google Scholar
Kutluay S., Yağmurlu N.M., Karakaş A.S., An effective numerical approach based on cubic hermite b-spline collocation method for solving the 1D heat conduction equation, New Trends in Mathematical Sciences, 10(4), 20–31, 2022.KutluayS.YağmurluN.M.KarakaşA.S.An effective numerical approach based on cubic hermite b-spline collocation method for solving the 1D heat conduction equationNew Trends in Mathematical Sciences10420312022Search in Google Scholar
Sun H., Zhang J., A high-order compact boundary value method for solving one-dimensional heat equations, Numerical Methods for Partial Differential Equations, 19(6), 846–857, 2003.SunH.ZhangJ.A high-order compact boundary value method for solving one-dimensional heat equationsNumerical Methods for Partial Differential Equations1968468572003Search in Google Scholar
Patel N., Pandya J.U., One-dimensional heat equation subject to both neumann and dirichlet initial boundary conditions and used a spline collocation method, Kalpa Publications in Computing, 2, 107–112, 2017.PatelN.PandyaJ.U.One-dimensional heat equation subject to both neumann and dirichlet initial boundary conditions and used a spline collocation methodKalpa Publications in Computing21071122017Search in Google Scholar
Tarmizi T., Safitri E., Munzir S., Ramli M., On the numerical solutions of a one-dimensional heat equation: spectral and crank nicolson method, AIP Conference Proceedings 2268(050006), 2020.TarmiziT.SafitriE.MunzirS.RamliM.On the numerical solutions of a one-dimensional heat equation: spectral and crank nicolson methodAIP Conference Proceedings22680500062020Search in Google Scholar
Yosaf A., Rehman S.U., Ahmad F., Ullah M.Z., Alshomrani A.S., Eight-order compact finite difference scheme for 1D heat conduction equation, Advances in Numerical Analysis, 2016(ID:8376061), 1–12, 2016.YosafA.RehmanS.U.AhmadF.UllahM.Z.AlshomraniA.S.Eight-order compact finite difference scheme for 1D heat conduction equationAdvances in Numerical Analysis2016(ID:8376061)1122016Search in Google Scholar
de Boor C., A Practical Guide to Splines, Applied Mathematical Sciences, Springer, USA, 2001.de BoorC.A Practical Guide to SplineApplied Mathematical SciencesSpringerUSA2001Search in Google Scholar
de Boor C., On calculating with b-splines, Journal of Approximation Theory, 6(1), 50–62, 1972.de BoorC.On calculating with b-splinesJournal of Approximation Theory6150621972Search in Google Scholar
Saka B., Dağ İ., Quartic b-spline collocation method to the numerical solutions of the Burgers’ equation, Chaos Solitons and Fractals, 32(3), 1125–1137, 2007.SakaB.Dağİ.Quartic b-spline collocation method to the numerical solutions of the Burgers’ equationChaos Solitons and Fractals323112511372007Search in Google Scholar
Dağ İ., Saka B., Boz A., B-spline galerkin methods for numerical solutions of the Burgers’ equation, Applied Mathematics and Computation, 166(3), 506–522, 2005.Dağİ.SakaB.BozA.B-spline galerkin methods for numerical solutions of the Burgers’ equationApplied Mathematics and Computation16635065222005Search in Google Scholar
Ramadan M.A., El-Danaf T.S, Abd Alaal F.E.I., A numerical solution of the Burgers’ equation using septic b-splines, Chaos Solitons and Fractals, 26(4), 1249–1258, 2005.RamadanM.A.El-DanafT.SAbd AlaalF.E.I.A numerical solution of the Burgers’ equation using septic b-splinesChaos Solitons and Fractals264124912582005Search in Google Scholar
Kumari A., Kukreja V.K., Error bounds for septic Hermite interpolation and its implementation to study modified Burgers’ equation, Numerical Algorithms, 89, 1799–1821, 2022.KumariA.KukrejaV.K.Error bounds for septic Hermite interpolation and its implementation to study modified Burgers’ equationNumerical Algorithms89179918212022Search in Google Scholar
Kumari A., Kukreja V.K., Shishkin mesh based septic Hermite interpolation algorithm for time-dependent singularly perturbed convection–diffusion models, Journal of Mathematical Chemistry, 60, 2029–2053, 2022.KumariA.KukrejaV.K.Shishkin mesh based septic Hermite interpolation algorithm for time-dependent singularly perturbed convection–diffusion modelsJournal of Mathematical Chemistry60202920532022Search in Google Scholar
Shakya P., Sinha R.K., A priori and a posteriori error estimates of finite-element approximations for elliptic optimal control problem with measure data, Optimal Control Applications and Methods, 40(2), 241–264, 2019.ShakyaP.SinhaR.K.A priori and a posteriori error estimates of finite-element approximations for elliptic optimal control problem with measure dataOptimal Control Applications and Methods4022412642019Search in Google Scholar