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65L05 Initial value problems (76 articles)

• Tomášek, Petr: On Euler methods for Caputo fractional differential equations. (English). Archivum Mathematicum, vol. 59 (2023), issue 3, pp. 287-294
• Martínek, Josef; Kučera, Václav: Numerical optimization of parameters in systems of differential equations. (English). In: Chleboun, J., Kůs, P., Papež, J., Rozložník, M., Segeth, K. and Šístek, J. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Jablonec nad Nisou, June 19-24, 2022. Institute of Mathematics CAS, Prague, 2023. pp. 123-132
• Pozza, Stefano; Van Buggenhout, Niel: The $\star$-product approach for linear ODEs: A numerical study of the scalar case. (English). In: Chleboun, J., Kůs, P., Papež, J., Rozložník, M., Segeth, K. and Šístek, J. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Jablonec nad Nisou, June 19-24, 2022. Institute of Mathematics CAS, Prague, 2023. pp. 187-198
• Hu, Guang-Da; Shao, Lizhen: Delay-dependent stability of linear multi-step methods for linear neutral systems. (English). Kybernetika, vol. 56 (2020), issue 3, pp. 543-558
• Hu, Guang-Da: Delay-dependent stability of Runge-Kutta methods for linear neutral systems with multiple delays. (English). Kybernetika, vol. 54 (2018), issue 4, pp. 718-735
• Chleboun, Jan; Mikeš, Karel: Identification of parameters in initial value problems for ordinary differential equations. (English). In: Chleboun, J., Přikryl, P., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 8-13, 2014. Institute of Mathematics AS CR, Prague, 2015. pp. 58-63
• Hu, Guang-Da: A modified version of explicit Runge-Kutta methods for energy-preserving. (English). Kybernetika, vol. 50 (2014), issue 5, pp. 838-847
• Vlasák, Miloslav; Roskovec, Filip: On Runge-Kutta, collocation and discontinuous Galerkin methods: Mutual connections and resulting consequences to the analysis. (English). In: Chleboun, J., Přikryl, P., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 8-13, 2014. Institute of Mathematics AS CR, Prague, 2015. pp. 231-236
• Minárová, Mária: Simulation of Indoor Humidity. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 53 (2014), issue 2, pp. 101-113
• Imoni, S. O.; Ikhile, M. N. O.: Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 53 (2014), issue 2, pp. 53-69
• Faragó, István: Convergence and stability constant of the theta-method. (English). In: Brandts, J., Korotov, S., Křížek, M., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2013, In honor of the 70th birthday of Karel Segeth. Proceedings. Prague, May 15-17, 2013. Institute of Mathematics AS CR, Prague, 2013. pp. 42-51
• Faragó, István; Havasi, Ágnes; Zlatev, Zahari: The convergence of explicit Runge-Kutta methods combined with Richardson extrapolation. (English). In: Brandts, J., Chleboun, J., Korotov, S., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2012, In honor of the 60th birthday of Michal Křížek. Proceedings. Prague, May 2-5, 2012. Institute of Mathematics AS CR, Prague, 2012. pp. 99-106
• Fischer, Cyril: Massive parallel implementation of ODE solvers. (English). In: Chleboun, J., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 3-8, 2012. Institute of Mathematics AS CR, Prague, 2013. pp. 75-80
• Okuonghae, R. I.; Ikhile, M. N. O.: The Numerical Solution of Stiff IVPs in ODEs Using Modified Second Derivative BDF. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 51 (2012), issue 1, pp. 51-77
• Okuonghae, R. I.; Ikhile, M. N. O.: A ($\alpha $)-Stable Linear Multistep Methods for Stiff IVPs in ODEs. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 50 (2011), issue 1, pp. 73-90
• Jánský, Jiří; Kundrát, Petr: The stability analysis of a discretized pantograph equation. (English). Mathematica Bohemica, vol. 136 (2011), issue 4, pp. 385-394
• Vlasák, Miloslav; Vlasáková, Zuzana: Derivation of BDF coefficients for equidistant time step. (English). In: Chleboun, J., Přikryl, P., Segeth, K. and Šístek, J. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 6-11, 2010. Institute of Mathematics AS CR, Prague, 2010. pp. 221-226
• Vitásek, Emil: $A$-stabilní metody libovolně vysokého řádu. (Czech) [$A$-stable methods of arbitrarily high order]. Pokroky matematiky, fyziky a astronomie, vol. 51 (2006), issue 1, pp. 61-68
• Lima, Pedro; Morgado, Luisa: Numerical approximation of singular boundary value problems for a nonlinear differential equation. (English). In: Fila, Marek, Handlovičová, A., Mikula, K., Medveď, Milan, Quittner, Pavol and Ševčovič, Daniel (eds.): Proceedings of Equadiff 11, International Conference on Differential Equations. Czecho-Slovak series, Bratislava, July 25-29, 2005. [Part 2] Minisymposia and contributed talks. Comenius University Press, Bratislava, 2007. pp. 201-211
• Hakl, R.; Lomtatidze, A.; Půža, B.: New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations. (English). Mathematica Bohemica, vol. 127 (2002), issue 4, pp. 509-524
• Jackiewicz, Zdzisław; Vermiglio, Rossana: Order conditions for partitioned Runge-Kutta methods. (English). Applications of Mathematics, vol. 45 (2000), issue 4, pp. 301-316
• Korbelář, Jan; Janovská, Drahoslava: Numerical model of a pine in a wind. (English). Applications of Mathematics, vol. 44 (1999), issue 6, pp. 459-468
• Mayer, Günter: Epsilon-inflation with contractive interval functions. (English). Applications of Mathematics, vol. 43 (1998), issue 4, pp. 241-254
• Kobza, Jiří: Numerical solution of some iterative differential equation. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 37 (1998), issue 1, pp. 47-55
• Pavluš, Miron; Podlubny, Igor: Parallel method for initial value problems for linear ordinary differential equations: speed up estimation. (English). Kybernetika, vol. 33 (1997), issue 3, pp. 279-290
• Podlubny, Igor: Parallel algorithms for initial and boundary value problems for linear ordinary differential equations and their systems. (English). Kybernetika, vol. 32 (1996), issue 3, pp. 251-260
• Jankowski, Tadeusz; Kwapisz, Marian: Convergence of numerical methods for systems of neutral functional-differential-algebraic equations. (English). Applications of Mathematics, vol. 40 (1995), issue 6, pp. 457-472
• Jackiewicz, Zdzislaw; Renaut, Rosemary Anne; Zennaro, Marino: Explicit two-step Runge-Kutta methods. (English). Applications of Mathematics, vol. 40 (1995), issue 6, pp. 433-456
• Spigler, Renato; Vianello, Marco: Semi-implicit discretization of abstract evolution equations. (English). In: Brunovský, Pavol and Medveď, Milan (eds.): Equadiff 8. Czech - Slovak Conference on Differential Equations and Their Applications. Bratislava, August 24-28, 1993. Mathematical Institute, Slovak Academy of Sciences, Bratislava, 1994. pp. 207-212
• Török, Csaba: A note on the Runge-Kutta method for stochastic differential equations. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 33 (1992), issue 1, pp. 121-124
• Kwapisz, Marian: On solving systems of differential algebraic equations. (English). Applications of Mathematics, vol. 37 (1992), issue 4, pp. 257-264
• Bremer, I.; Schneider, Klaus R.: A remark on solving large systems of equations in function spaces. (English). Aplikace matematiky, vol. 35 (1990), issue 6, pp. 494-498
• Jódar, Lucas; Navarro, E.: On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate. (English). Aplikace matematiky, vol. 34 (1989), issue 6, pp. 429-438
• Grossmann, Ch.: Quasi-Newton updates in row-methods for avoiding Jacobians. (English). In: Kurzweil, Jaroslav (ed.): Equadiff 7. Proceedings of the 7th Czechoslovak Conference on Differential Equations and Their Applications held in Prague, 1989. BSB B.G. Teubner Verlagsgesellschaft, Leipzig, 1990. pp. 252-255
• Jankowski, Tadeusz: On numerical solution of ordinary differential equations with discontinuities. (English). Aplikace matematiky, vol. 33 (1988), issue 6, pp. 487-492
• Valková, Anna: On total truncation error estimation for the one-step method. (English). Aplikace matematiky, vol. 32 (1987), issue 3, pp. 177-185
• Holický, Petr: On a simulation of the oscillation excited by a random force. (English). Kybernetika, vol. 22 (1986), issue 2, pp. 176-188
• Stetter, Hans J.: Algorithms for the inclusion of solutions of ordinary initial value problems. (English). In: Vosmanský, Jaromír and Zlámal, Miloš (eds.): Equadiff 6. Proceedings of the International Conference on Differential Equations and Their Applications held in Brno, Czechoslovakia, Aug. 26 - 30, 1985. J. E. Purkyně University, Department of Mathematics, Brno, 1986. pp. 85-94
• Axelsson, Owe: Stability and error estimates valid for infinite time, for strongly monotone and infinitely stiff evolution equations. (English). In: Vosmanský, Jaromír and Zlámal, Miloš (eds.): Equadiff 6. Proceedings of the International Conference on Differential Equations and Their Applications held in Brno, Czechoslovakia, Aug. 26 - 30, 1985. J. E. Purkyně University, Department of Mathematics, Brno, 1986. pp. [275]-284
• Huťa, Anton; Penjak, Vladimír: A contribution to Runge-Kutta formulas of the 7th order with rational coefficients for systems of differential equations of the first order. (English). Aplikace matematiky, vol. 29 (1984), issue 6, pp. 411-422
• Beneš, Karel: Simulation of analog computer in solving non-linear differential equations by a digital computer. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 23 (1984), issue 1, pp. 141-151
• Vanselow, Reiner: Erweiterung des $G$-Stabilitätsbegriffes auf die Klasse der linearen Mehrschrittblockverfahren. (German) [Extension of the $G$-stability concept to the class of the linear multistep block methods]. Aplikace matematiky, vol. 28 (1983), issue 1, pp. 9-20
• Vanselow, Reiner: Explizite Konstruktion von linearen Mehrschrittblockverfahren. (German) [Explicit construction of linear multistep block methods]. Aplikace matematiky, vol. 28 (1983), issue 1, pp. 1-8
• Jackiewicz, Zdzisław: Global error estimation in the numerical solution of retarded differential equations by Euler's method. (English). Aplikace matematiky, vol. 28 (1983), issue 3, pp. 177-185
• Beneš, Karel: Increase of accuracy in solving differential equations with singularities of the type $\frac{0}{0}$ by a right choice of an additional term. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 22 (1983), issue 1, pp. 167-174
• Kobza, Jiří: Second derivative linear multistep formula and its stability on the imaginary axis. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 22 (1983), issue 1, pp. 131-142
• Roubíček, Tomáš: Unconditional stability of difference formulas. (English). Aplikace matematiky, vol. 28 (1983), issue 2, pp. 81-90
• Huťa, Anton; Strehmel, Karl: Construction of explicit and generalized Runge-Kutta formulas of arbitrary order with rational parameters. (English). Aplikace matematiky, vol. 27 (1982), issue 4, pp. 259-276
• Beneš, Karel: Increase of accuracy in machine computation of some differential equations having variable coefficients and of some nonlinear differential equations. (English). Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika, vol. 21 (1982), issue 1, pp. 133-147
• Beneš, Karel: Programming of differential equations with singularitiens of the type $\frac{0}{0}$ in using the extension to power series. (English). Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika, vol. 21 (1982), issue 1, pp. 119-131
• Huťa, Anton: Algorithm for construction of explicit $n$-order Runge-Kutta formulas for the systems of differential equations of the 1st order. (English). In: Greguš, Michal (ed.): Equadiff 5. Proceedings of the Fifth Czechoslovak Conference on Differential Equations and Their Applications held in Bratislava, August 24-28, 1981. BSB B.G. Teubner Verlagsgesellschaft, Leipzig, 1982. pp. 140-144
• Jackiewicz, Zdzisław; Kwapisz, Marian: On numerical integration of implicit ordinary differential equations. (English). Aplikace matematiky, vol. 26 (1981), issue 2, pp. 97-110
• Ismail, Hassan Nasr Ahmed: Generalized periodic overimplicit multistep methods (GPOM methods). (English). Aplikace matematiky, vol. 24 (1979), issue 4, pp. 250-272
• Ismail, Hassan Nasr Ahmed: Necessary conditions for the convergence of the generalized periodic overimplicit multistep method. (English). Aplikace matematiky, vol. 24 (1979), issue 4, pp. 273-283
• Jankowski, Tadeusz: Some remarks on numerical solution of initial problems for systems of differential equations. (English). Aplikace matematiky, vol. 24 (1979), issue 6, pp. 421-426
• Taufer, J.; Vitásek, E.: $A$-stability and numerical solution of abstract differential equations. (English). In: Fábera, Jiří (ed.): Equadiff IV. Czechoslovak Conference on Differential Equations and Their Applications. Proceedings, Prague, August 22-26, 1977. Springer-Verlag, Berlin, 1979. pp. [415]-423
• Višňák, Karel: A-stable block implicit methods containing second derivatives. (English). Czechoslovak Mathematical Journal, vol. 27 (1977), issue 1, pp. 14-42
• Pirč, Viktor: On the possibility of calculation of zero points of solutions of differential equations of the second order. (English). Aplikace matematiky, vol. 22 (1977), issue 3, pp. 176-179
• Kobza, Jiří: Stability of the second derivative linear multistep formulas. (English). Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika, vol. 16 (1977), issue 1, pp. 167-184
• Scholz, Siegfried: Runge-Kutta-Verfahren mit festen und variablen Parametern zur Lösung von Systemen gewöhnlicher Differentialgleichungen 1. Ordnung. (German) [The Runge-Kutta method with fixed and variable parameters for solution of systems of first-order ordinary differential equations]. Aplikace matematiky, vol. 20 (1975), issue 3, pp. 166-185
• Kobza, Jiří: Методы типа Адамса с вторыми производными. (Russian) [Methods of Adams type with second derivatives]. Aplikace matematiky, vol. 20 (1975), issue 6, pp. 389-405
• Nassif, N. R.: On a finite-element collocation method which reproduces the Padé table. (English). Acta Universitatis Carolinae. Mathematica et Physica, vol. 15 (1974), issue 1, pp. 105-109
• Fage, M. K.; Maximey, G. A.: On approximate solution of systems of linear ordinary differential equations. (English). Acta Universitatis Carolinae. Mathematica et Physica, vol. 15 (1974), issue 1, pp. 17
• Spijker, M. N.: Optimum error estimates for finite-difference methods. (English). Acta Universitatis Carolinae. Mathematica et Physica, vol. 15 (1974), issue 1, pp. 159-164
• Práger, M.; Taufer, J.; Vitásek, E.: Overimplicit methods for the solution of evolution problems. (English). Acta Universitatis Carolinae. Mathematica et Physica, vol. 15 (1974), issue 1, pp. 125-133
• Jankovič, V.: A parallel method of solution of the differential equations by the formulas containing higher derivatives. (English). Acta Universitatis Carolinae. Mathematica et Physica, vol. 15 (1974), issue 1, pp. 55-57
• Kubíček, M.; Višňák, K.: Two classes of numerical methods for stiff problems. (English). Acta Universitatis Carolinae. Mathematica et Physica, vol. 15 (1974), issue 1, pp. 63-66
• Hlaváček, Ivan: On a semi-variational method for parabolic equations. II. (English). Aplikace matematiky, vol. 18 (1973), issue 1, pp. 43-64
• Práger, Milan; Taufer, Jiří; Vitásek, Emil: Overimplicit multistep methods. (English). Aplikace matematiky, vol. 18 (1973), issue 6, pp. 399-421
• Popoviciu, Tiberiu: Application de la théorie des fonctions convexes d'ordre supérieur à l'étude de certains procédés d'intégration numérique des équations différentielles. (French) [Applications of the theory of higher order convex functions in the study of certain numerical methods of solving differential equations]. In: Ráb, Miloš and Vosmanský, Jaromír (eds.): Proceedings of Equadiff III. 3rd Czechoslovak Conference on Differential Equations and Their Applications. Brno, Czechoslovakia, August 28 - September 1, 1972. Univ. J. E. Purkyně - Přírodovědecká fakulta, Brno, 1973. pp. 241-245
• Hlaváček, Ivan: On finite element procedures of high order accuracy for parabolic equations. (English). In: Ráb, Miloš and Vosmanský, Jaromír (eds.): Proceedings of Equadiff III. 3rd Czechoslovak Conference on Differential Equations and Their Applications. Brno, Czechoslovakia, August 28 - September 1, 1972. Univ. J. E. Purkyně - Přírodovědecká fakulta, Brno, 1973. pp. 225
• Volkov, E. A.: On two-sided difference methods for ordinary differential equations. (English). In: Ráb, Miloš and Vosmanský, Jaromír (eds.): Proceedings of Equadiff III. 3rd Czechoslovak Conference on Differential Equations and Their Applications. Brno, Czechoslovakia, August 28 - September 1, 1972. Univ. J. E. Purkyně - Přírodovědecká fakulta, Brno, 1973. pp. 81-87
• Práger, Milan; Taufer, Jiří; Vitásek, Emil: Some new methods for numerical solution of initial value problems. (English). In: Ráb, Miloš and Vosmanský, Jaromír (eds.): Proceedings of Equadiff III. 3rd Czechoslovak Conference on Differential Equations and Their Applications. Brno, Czechoslovakia, August 28 - September 1, 1972. Univ. J. E. Purkyně - Přírodovědecká fakulta, Brno, 1973. pp. 247-253
• Voňka, Petr: Stability and local error of difference methods for the solution of the ordinary differential equation of the first order. (English). Aplikace matematiky, vol. 17 (1972), issue 1, pp. 18-27
• Vitásek, Emil: Numerical stability in solution of ordinary differential equations. (English). Aplikace matematiky, vol. 13 (1968), issue 2, pp. 203-207
• Gurega, Ján; Kostolanský, Eduard: Решение системы обыкновенных дифференциальных уравнений на быстродействующей вычислительной машине методом Нордсика. (Russian) [Solution of a system of ordinary differential equations on a computer by the Nordsieck method]. Aplikace matematiky, vol. 10 (1965), issue 3, pp. 217-221