المؤلفون: Onitsuka, Masakazu

مصطلحات موضوعية: keyword:approximate solution, keyword:variable coefficients, keyword:generalized logistic equation, keyword:conditional Ulam stability, keyword:limit cycle, msc:34A12, msc:34C05, msc:34C07, msc:34D10, msc:39A30

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Relation: mr:MR4563019; zbl:Zbl 07675577; reference:[1] Anderson, D.R., Onitsuka, M.: Hyers-Ulam stability for differential systems with $2\times 2$ constant coefficient matrix.Results Math. 77 (2022), 23, Paper No. 136. MR 4420286, 10.1007/s00025-022-01671-y; reference:[2] Benterki, R., Jimenez, J., Llibre, J.: Limit cycles of planar discontinuous piecewise linear Hamiltonian systems without equilibria separated by reducible cubics.Electron. J. Qual. Theory Differ. Equ. 2021 (2021), 38 pp., Paper No. 69. MR 4389338; reference:[3] Boukoucha, R.: Limit cycles explicitly given for a class of a differential systems.Nonlinear Stud. 28 (2) (2021), 375–387. MR 4328117; reference:[4] Castro, L.P., Simões, A.M.: A Hyers-Ulam stability analysis for classes of Bessel equations.Filomat 35 (13) (2021), 4391–4403. MR 4365541, 10.2298/FIL2113391C; reference:[5] Deepa, S., Bowmiya, S., Ganesh, A., Govindan, V., Park, C., Lee, J.: Mahgoub transform and Hyers-Ulam stability of n-th order linear differential equations.AIMS Math. 7 (4) (2022), 4992–5014. MR 4357984, 10.3934/math.2022278; reference:[6] Devi, A., Kumar, A.: Hyers-Ulam stability and existence of solution for hybrid fractional differential equation with $p$-Laplacian operator.Chaos Solitons Fractals 156 (2022), 8 pp., Paper No. 111859. MR 4379223; reference:[7] Diab, Z., Guirao, J.L.G., Vera, J.A.: On the limit cycles for a class of generalized Liénard differential systems.Dyn. Syst. 37 (1) (2022), 1–8. MR 4408073, 10.1080/14689367.2021.1993144; reference:[8] Fečkan, M., Li, Q., Wang, J.: Existence and Ulam-Hyers stability of positive solutions for a nonlinear model for the Antarctic Circumpolar Current.Monatsh. Math. 197 (3) (2022), 419–434. MR 4389128, 10.1007/s00605-021-01618-5; reference:[9] Galias, Z., Tucker, W.: The Songling system has exactly four limit cycles.Appl. Math. Comput. 415 (2022), 8 pp., Paper No. 126691. MR 4327335; reference:[10] Gong, S., Han, M.: An estimate of the number of limit cycles bifurcating from a planar integrable system.Bull. Sci. Math. 176 (2022), 39 pp., Paper No. 103118. MR 4395271; reference:[11] Huang, J., Li, J.: On the number of limit cycles in piecewise smooth generalized Abel equations with two asymmetric zones.Nonlinear Anal. Real World Appl. 66 (2022), 17 pp., Paper No. 103551. MR 4389045; reference:[12] Jung, S.-M., Ponmana Selvan, A., Murali, R.: Mahgoub transform and Hyers–Ulam stability of first-order linear differential equations.J. Math. Inequal. 15 (3) (2021), 1201–1218. MR 4364669, 10.7153/jmi-2021-15-80; reference:[13] Kelley, W.G., Peterson, A.C.: The Theory of Differential Equations: Classical and Qualitative.Springer, New York, 2010, Second Edition, Universitext. MR 2640364; reference:[14] Li, J., Han, M.: Planar integrable nonlinear oscillators having a stable limit cycle.J. Appl. Anal. Comput. 12 (2) (2022), 862–867. MR 4398697; reference:[15] Nam, Y.W.: Hyers-Ulam stability of loxodromic Möbius difference equation.Appl. Math. Comput. 356 (2019), 119–136. MR 3933980, 10.1016/j.amc.2019.03.033; reference:[16] Onitsuka, M.: Approximate solutions of generalized logistic equation.submitted.; reference:[17] Onitsuka, M.: Conditional Ulam stability and its application to the logistic model.Appl. Math. Lett. 122 (2021), 7 pp., Paper No. 107565. MR 4296927; reference:[18] Onitsuka, M.: Conditional Ulam stability and its application to von Bertalanffy growth model.Math. Biosci. Eng. 19 (3) (2022), 2819–2834. MR 4364436, 10.3934/mbe.2022129; reference:[19] Onitsuka, M., El-Fassi, Iz.: On approximate solutions of a class of Clairaut’s equations.Appl. Math. Comput. 428 (2022), 13 pp., Paper No. 127205. MR 4421006, 10.1016/j.amc.2022.127205; reference:[20] Sugie, J., Ishibashi, K.: Limit cycles of a class of Liénard systems derived from state-dependent impulses.Nonlinear Anal. Hybrid Syst. 45 (2022), 16 pp., Paper No. 101188. MR 4399231

الاتاحة: http://hdl.handle.net/10338.dmlcz/151553

المؤلفون: Vinogradova, Polina, Zarubin, Anatoli

مصطلحات موضوعية: keyword:approximate solution, keyword:error estimate, keyword:Galerkin method, keyword:heat convection equation, keyword:orthogonal projection, keyword:viscous fluid, msc:35K90, msc:35Q35, msc:65J10, msc:65M15, msc:65M60

وصف الملف: application/pdf

Relation: mr:MR2891306; zbl:Zbl 1249.65119; reference:[1] Agmon, S.: On the eigenfunctions and on the eigenvalue of general elliptic boundary value problems.Commun. Pure Appl. Math. 15 (1962), 119-147. MR 0147774, 10.1002/cpa.3160150203; reference:[2] Ambethkar, V.: Numerical solutions of heat and mass transfer effects of an unsteady MHD free convective flow past an infinite vertical plate with constant suction.J. Naval Arch. Marine Eng. 5 (2008), 28-36.; reference:[3] Babskii, V. G., Kopachevskii, N. D., Myshkis, A. D., Slobozhanin, L. A., Tyuptsov, A. D.: Fluid Mechanics of Weightlessness.Nauka Moscow (1976), Russian.; reference:[4] Beckenbach, E., Bellman, R.: Inequalities.Springer Berlin (1965). Zbl 0186.09605, MR 0192009; reference:[5] Curry, J. H., Herring, J. R., Loncaric, J., Orszag, S. A.: Order and disorder in two- and three-dimensional Bénard convection.J. Fluid Mech. 147 (1984), 1-38. Zbl 0547.76093, 10.1017/S0022112084001968; reference:[6] Daly, B. J.: A numerical study of turbulence transitions in convective flow.J. Fluid Mech. 64 (1974), 129-165. Zbl 0282.76050, 10.1017/S0022112074002047; reference:[7] Gershuni, G. Z., Zhuhovitsky, E. M.: Convective Stability of Incompressible Fluid.Nauka Moscow (1972), Russian.; reference:[8] Glushko, V. P., Krejn, S. G.: Inequalities for the norms of derivative in spaces $L_p$ with weight.Sibirsk. Mat. Zh. 1 (1960), 343-382 Russian. MR 0133681; reference:[9] Krejn, S. G.: Linear Differential Equations in Banach Spaces. Trans. Math. Monographs, Vol. 29.AMS Providence (1972).; reference:[10] Ladyzhenskaya, O. A.: The Mathematical Theory of Viscous Incompressible Flow.Gordon and Breach New York (1969). Zbl 0184.52603, MR 0254401; reference:[11] Ladyzhenskaya, O. A., Solonnikov, V. A., Ural'tseva, N. N.: Linear and Quasilinear Equations of Parabolic Type.Nauka Moscow (1967), English transl.: Trans. Math. Monographs, Vol. 23 AMS Rhode Island (1968). Zbl 0164.12302; reference:[12] Shinbrot, M., Kotorynski, W. P.: The initial value problem for a viscous heat-conducting equations.J. Math. Anal. Appl. 45 (1974), 1-22. MR 0361474, 10.1016/0022-247X(74)90115-2; reference:[13] Solonnikov, V. A.: On estimates of the solutions of elliptic and parabolic systems in $L_p$.Tr. MIAN SSSR 102 (1967), 137-160 Russian. MR 0228809; reference:[14] Temam, R.: Navier-Stokes Equations. Theory and Numerical Analysis. Rev. ed.North-Holland Publishing Company Amsterdam (1979). Zbl 0426.35003; reference:[15] Vinogradova, P., Zarubin, A.: Projection method for Cauchy problem for operator-differential equation.Numer. Funct. Anal. Optim. 30 (2009), 148-167. MR 2492080, 10.1080/01630560902735132; reference:[16] Werne, J., DeLuca, E. E., Rosner, R., Cattaneo, F.: Numerical simulation of soft and hard turbulence: preliminary results for two-dimensional convection.Phys. Rev. Lett. 64 (1990), 2370-2373. 10.1103/PhysRevLett.64.2370

الاتاحة: http://hdl.handle.net/10338.dmlcz/141819

المؤلفون: Moszyński, Krzysztof

مصطلحات موضوعية: keyword:Fourier expansion, keyword:orthogonal polynomials on $L^2(\Omega)$ space, keyword:approximate solution of linear algebraic equations, keyword:Richardson iteration, keyword:preconditioning, keyword:polynomial methods, keyword:numerical examples, msc:65F10

وصف الملف: application/pdf

Relation: mr:MR1185798; zbl:Zbl 0802.65032; reference:[1] Doan Van Ban, Moszyński K., Pokrzywa A.: Semiiterative methods for linear equations.Matematyka Stosowana-Applied Mathematics, Vol. 35, Warszawa, 1992. MR 1221221; reference:[2] Gaier D.: Lectures on Complex Approximation.Birkhäuser, 1989. MR 0894920; reference:[3] Reichel L.: Polynomials by conformal mapping for the Richardson iteration method for complex linear systems.SIAM NA 25 no. 6 (1988), 1359-1368. Zbl 0692.65011, MR 0972459, 10.1137/0725077

الاتاحة: http://hdl.handle.net/10338.dmlcz/104521

المؤلفون: Feireisl, Eduard

مصطلحات موضوعية: keyword:thin plate, keyword:simply supported, keyword:existence, keyword:infinitely many nonzero time-periodic solutions, keyword:Ljusternik-Schnirelman theory, keyword:approximate solution, msc:35B10, msc:35L70, msc:58E05, msc:73K12, msc:74H45, msc:74K20

وصف الملف: application/pdf

Relation: mr:MR0940708; zbl:Zbl 0648.73024; reference:[1] H. Amann G. Mancini: Some applications of monotone operator theory to resonance problems.Nonlinear Anal. 3 (1979), 815-830. MR 0548954, 10.1016/0362-546X(79)90050-6; reference:[2] K. C. Chang L. Sanchez: Nontrivial periodic solutions of a nonlinear beam equation.Math. Meth. in the Appl. Sci. 4 (1982), 194-205. MR 0659037, 10.1002/mma.1670040113; reference:[3] E. Feireisl: On periodic solutions of a beam equation.(Czech.). Thesis, Fac. Math. Phys. of Charles Univ., Prague 1982.; reference:[4] V. Lovicar: Free vibrations for the equation $u_{tt} - u_{xx} + f(u) = 0$ with f sublinear.Proceedings of EQUADIFF 5, Teubner Texte zur Mathematik, Band 47, 228-230. MR 0715981; reference:[5] P. H. Rabinowitz: Free vibrations for a semilinear wave equation.Comm. Pure Appl. Math. 31 (1978), 31-68. Zbl 0341.35051, MR 0470378, 10.1002/cpa.3160310103

الاتاحة: http://hdl.handle.net/10338.dmlcz/104290

المؤلفون: Ženíšek, Alexander

مصطلحات موضوعية: keyword:Existence, keyword:uniqueness, keyword:variational problem, keyword:Biot’s model, keyword:compactness method, keyword:approximate solution, keyword:finite elements, keyword:Euler’s backward method, msc:35A05, msc:35A15, msc:35A35, msc:35G05, msc:65N30, msc:73Q05

وصف الملف: application/pdf

Relation: mr:MR0747212; zbl:Zbl 0557.35005; reference:[1] M. A. Biot: General theory of three-dimensional consolidation.J. Appl. Phys. 12 (1941), p. 155. 10.1063/1.1712886; reference:[2] J. R. Booker: A numerical method for the solution of Bioťs consolidation theory.Quart. J. Mech. Appl. Math. 26 (1973), 457-470. 10.1093/qjmam/26.4.457; reference:[3] J. Céa: Optimization.Dunod, Paris, 1971. Zbl 0231.94026, MR 0298892; reference:[4] A. Kufner O. John S. Fučík: Function Spaces.Academia, Prague, 1977. MR 0482102; reference:[5] J. L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires.Dunod and Gauthier-Villars, Paris, 1969. Zbl 0189.40603, MR 0259693; reference:[6] R. Теmаm: Navier-Stokes Equations.North-Holland, Amsterdam, 1977.; reference:[7] M. Zlámal: Curved elements in the finite element method. I.SIAM J. Numer. Anal. 10 (1973), 229-240. MR 0395263, 10.1137/0710022; reference:[8] M. Zlámal: Finite element solution of quasistationary nonlinear magnetic field.R. A.I.R.O. Anal. Num. 16 (1982), 161-191. MR 0661454; reference:[9] A. Ženíšek: Finite element methods for coupled thermoelasticity and coupled consolidation of clay.(To appear.) MR 0743885; reference:[10] K. Rektorys: The Method of Discretization in Time and Partial Differential Equations.D. Reidel Publishing Company, Dordrecht - SNTL, Prague, 1982. Zbl 0522.65059, MR 0689712

الاتاحة: http://hdl.handle.net/10338.dmlcz/104085

المؤلفون: Ženíšek, Alexander

مصطلحات موضوعية: keyword:generalized Bell’s $C^m$-elements, keyword:approximate solution, keyword:rate of convergence, msc:35A35, msc:35J40, msc:65M99, msc:65N30, msc:65N99

وصف الملف: application/pdf

Relation: mr:MR0502072; zbl:Zbl 0404.35041; reference:[1] Bramble J. H., Zlámal M.: Triangular elements in the finite element method.Math. Соmр. 24 (1970), 809-820. MR 0282540; reference:[2] Ciarlet P. G., Raviart P. A.: The combined effect of curved boundaries and numerical integration in isoparametric finite element methods.In: The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz, Editor), pp. 409-474, Academic Press, New York 1972. Zbl 0262.65070, MR 0421108; reference:[3] Ciarlet P. G.: Numerical Analysis of the Finite Element Method.Université de Montréal, 1975. MR 0495010; reference:[4] Holuša L., Kratochvíl J., Zlámal M., Ženíšek A.: The Finite Element Method.Technical Report. Computing Center of the Technical University of Brno, 1970. (In Czech.); reference:[5] Kratochvíl J., Ženíšek A., Zlámal M.: A simple algorithm for the stiffness matrix of triangular plate bending finite elements.Int. J. numer. Meth. Engng. 3 (1971), 553 - 563. 10.1002/nme.1620030409; reference:[6] Mansfield L.: Approximation of the boundary in the finite element solution of fourth order problems.SIAM J. Numer. Anal. 15 (1978), the June issue. Zbl 0391.65047, MR 0471373, 10.1137/0715037; reference:[7] Nečas J.: Les méthodes directes en théorie des équations elliptiques.Academia, Prague, 1967. MR 0227584; reference:[8] Stroud A. H.: Approximate Calculation of Multiple Integrals.Prentice-Hall., Englewood Cliffs, N. J., 1971. Zbl 0379.65013, MR 0327006; reference:[9] Zlámal M.: The finite element method in domains with curved boundaries.Int. J. numer. Meth. Engng. 5 (1973), 367-373. MR 0395262, 10.1002/nme.1620050307; reference:[10] Zlámal M.: Curved elements in the finite element method. I.SIAM J. Numer. Anal. 10(1973), 229-240. MR 0395263, 10.1137/0710022; reference:[11] Zlámal M.: Curved elements in the finite element method. II.SlAM J. Numer. Anal. 1.1 (1974), 347-362. MR 0343660, 10.1137/0711031; reference:[12] Ženíšek A.: Interpolation polynomials on the triangle.Numer. Math. 15 (1970), 283 - 296. MR 0275014, 10.1007/BF02165119

الاتاحة: http://hdl.handle.net/10338.dmlcz/103761