메뉴 건너뛰기




Volumn 2013, Issue , 2013, Pages

An efficient approach for solving nonlinear troesch's and bratu's problems by wavelet analysis method

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRAIC EQUATIONS; CHEBYSHEV; CONVERGENCE ANALYSIS; EXACT SOLUTION; NONLINEAR PROBLEMS; OPERATIONAL MATRIX OF DERIVATIVES; WAVELET ANALYSIS METHOD; WAVELET BASIS FUNCTIONS;

EID: 84884243573     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2013/825817     Document Type: Article
Times cited : (11)

References (39)
  • 3
    • 0040384921 scopus 로고
    • On the closed form solution of Troesch's problem
    • MR0416046 10.1016/0021-9991(76)90026-7 ZBL0334.65062
    • Roberts S. M., Shipman J. S., On the closed form solution of Troesch's problem. Journal of Computational Physics 1976 21 3 291 304 MR0416046 10.1016/0021-9991(76)90026-7 ZBL0334.65062
    • (1976) Journal of Computational Physics , vol.21 , Issue.3 , pp. 291-304
    • Roberts, S.M.1    Shipman, J.S.2
  • 4
    • 0039684959 scopus 로고
    • On the confinement of a plasma by magnetostatic fields
    • 2-s2.0-0039684959
    • Weibel E. S., On the confinement of a plasma by magnetostatic fields. Physics of Fluids 1959 2 1 52 56 2-s2.0-0039684959
    • (1959) Physics of Fluids , vol.2 , Issue.1 , pp. 52-56
    • Weibel, E.S.1
  • 5
    • 33748116425 scopus 로고
    • Intrinsic difficulties in the numerical solution of a boundary value problem
    • Redondo Beach, Calif, USA TRW Inc
    • Troesch B. A., Intrinsic difficulties in the numerical solution of a boundary value problem. Internal Report 1960 142 Redondo Beach, Calif, USA TRW Inc.
    • (1960) Internal Report , Issue.142
    • Troesch, B.A.1
  • 6
    • 0005338184 scopus 로고    scopus 로고
    • An algorithm for solving boundary value problems
    • 10.1006/jcph.2000.6452 MR1752614 ZBL0959.65091
    • Deeba E., Khuri S. A., Xie S., An algorithm for solving boundary value problems. Journal of Computational Physics 2000 159 2 125 138 10.1006/jcph.2000.6452 MR1752614 ZBL0959.65091
    • (2000) Journal of Computational Physics , vol.159 , Issue.2 , pp. 125-138
    • Deeba, E.1    Khuri, S.A.2    Xie, S.3
  • 7
    • 34248395626 scopus 로고    scopus 로고
    • An efficient algorithm for solving Troesch's problem
    • 10.1016/j.amc.2006.11.161 MR2330227 ZBL1122.65373
    • Feng X., Mei L., He G., An efficient algorithm for solving Troesch's problem. Applied Mathematics and Computation 2007 189 1 500 507 10.1016/j.amc.2006.11.161 MR2330227 ZBL1122.65373
    • (2007) Applied Mathematics and Computation , vol.189 , Issue.1 , pp. 500-507
    • Feng, X.1    Mei, L.2    He, G.3
  • 8
    • 33845753056 scopus 로고    scopus 로고
    • Variational iteration method for solving nonlinear boundary value problems
    • 10.1016/j.amc.2006.05.138 MR2294094 ZBL1110.65068
    • Momani S., Abuasad S., Odibat Z., Variational iteration method for solving nonlinear boundary value problems. Applied Mathematics and Computation 2006 183 2 1351 1358 10.1016/j.amc.2006.05.138 MR2294094 ZBL1110.65068
    • (2006) Applied Mathematics and Computation , vol.183 , Issue.2 , pp. 1351-1358
    • Momani, S.1    Abuasad, S.2    Odibat, Z.3
  • 9
    • 28244446638 scopus 로고    scopus 로고
    • A numerical algorithm for solving Troesch's problem
    • 10.1080/0020716022000009228 MR1983307 ZBL1022.65084
    • Khuri S. A., A numerical algorithm for solving Troesch's problem. International Journal of Computer Mathematics 2003 80 4 493 498 10.1080/0020716022000009228 MR1983307 ZBL1022.65084
    • (2003) International Journal of Computer Mathematics , vol.80 , Issue.4 , pp. 493-498
    • Khuri, S.A.1
  • 10
    • 80051583591 scopus 로고    scopus 로고
    • Troesch's problem: A B-spline collocation approach
    • 10.1016/j.mcm.2011.04.030 MR2834597
    • Khuri S. A., Sayfy A., Troesch's problem: a B-spline collocation approach. Mathematical and Computer Modelling 2011 54 9-10 1907 1918 10.1016/j.mcm.2011.04.030 MR2834597
    • (2011) Mathematical and Computer Modelling , vol.54 , Issue.9-10 , pp. 1907-1918
    • Khuri, S.A.1    Sayfy, A.2
  • 11
    • 84863599859 scopus 로고    scopus 로고
    • The sinc-Galerkin method for solving Troesch's problem
    • 10.1016/j.mcm.2011.11.071 MR2950862 ZBL1255.65153
    • Zarebnia M., Sajjadian M., The sinc-Galerkin method for solving Troesch's problem. Mathematical and Computer Modelling 2012 56 9-10 218 228 10.1016/j.mcm.2011.11.071 MR2950862 ZBL1255.65153
    • (2012) Mathematical and Computer Modelling , vol.56 , Issue.9-10 , pp. 218-228
    • Zarebnia, M.1    Sajjadian, M.2
  • 12
    • 37349013500 scopus 로고    scopus 로고
    • A new algorithm for calculating one-dimensional differential transform of nonlinear functions
    • 10.1016/j.amc.2007.05.026 MR2381259 ZBL1132.65062
    • Chang S.-H., Chang I.-L., A new algorithm for calculating one-dimensional differential transform of nonlinear functions. Applied Mathematics and Computation 2008 195 2 799 805 10.1016/j.amc.2007.05.026 MR2381259 ZBL1132.65062
    • (2008) Applied Mathematics and Computation , vol.195 , Issue.2 , pp. 799-805
    • Chang, S.-H.1    Chang, I.-L.2
  • 13
    • 77955279417 scopus 로고    scopus 로고
    • A variational iteration method for solving Troesch's problem
    • 10.1016/j.cam.2010.04.018 MR2652150 ZBL1191.65101
    • Chang S.-H., A variational iteration method for solving Troesch's problem. Journal of Computational and Applied Mathematics 2010 234 10 3043 3047 10.1016/j.cam.2010.04.018 MR2652150 ZBL1191.65101
    • (2010) Journal of Computational and Applied Mathematics , vol.234 , Issue.10 , pp. 3043-3047
    • Chang, S.-H.1
  • 14
    • 37349011714 scopus 로고
    • On the conversion of boundary-value problems into stable initial-value problems via several invariant imbedding algorithms
    • New York, NY, USA Academic Press MR0416044 ZBL0335.65032
    • Scott M. R., Aziz A. K., On the conversion of boundary-value problems into stable initial-value problems via several invariant imbedding algorithms. Numerical Solutions of Boundary-Value Problems for Ordinary Differential Equations 1975 New York, NY, USA Academic Press 89 146 MR0416044 ZBL0335.65032
    • (1975) Numerical Solutions of Boundary-Value Problems for Ordinary Differential Equations , pp. 89-146
    • Scott, M.R.1    Aziz, A.K.2
  • 15
    • 1142306260 scopus 로고
    • Solution of Troesch's two-point boundary value problem by a combination of techniques
    • Roberts S. M., Shipman J. S., Solution of Troesch's two-point boundary value problem by a combination of techniques. Journal of Computational Physics 1972 10 232 241
    • (1972) Journal of Computational Physics , vol.10 , pp. 232-241
    • Roberts, S.M.1    Shipman, J.S.2
  • 16
    • 84884241934 scopus 로고    scopus 로고
    • New explicit solutions for Troesch's boundary value problem
    • MR2475859 ZBL1191.34025
    • Bougoffa L., Al-khadhi M. A., New explicit solutions for Troesch's boundary value problem. Applied Mathematics & Information Sciences 2009 3 1 89 96 MR2475859 ZBL1191.34025
    • (2009) Applied Mathematics & Information Sciences , vol.3 , Issue.1 , pp. 89-96
    • Bougoffa, L.1    Al-Khadhi, M.A.2
  • 17
    • 77951003631 scopus 로고    scopus 로고
    • Application of an approximate analytical method to nonlinear Troesch's problem
    • MR2544649
    • Mirmoradi S. H., Hosseinpour I., Ghanbarpour S., Barari A., Application of an approximate analytical method to nonlinear Troesch's problem. Applied Mathematical Sciences 2009 3 29-32 1579 1585 MR2544649
    • (2009) Applied Mathematical Sciences , vol.3 , Issue.29-32 , pp. 1579-1585
    • Mirmoradi, S.H.1    Hosseinpour, I.2    Ghanbarpour, S.3    Barari, A.4
  • 18
    • 79955804712 scopus 로고    scopus 로고
    • An efficient analytic approach for solving two-point nonlinear boundary value problems by homotopy analysis method
    • 10.1002/mma.1416 MR2828745 ZBL1226.34021
    • Hassan H. N., El-Tawil M. A., An efficient analytic approach for solving two-point nonlinear boundary value problems by homotopy analysis method. Mathematical Methods in the Applied Sciences 2011 34 8 977 989 10.1002/mma.1416 MR2828745 ZBL1226.34021
    • (2011) Mathematical Methods in the Applied Sciences , vol.34 , Issue.8 , pp. 977-989
    • Hassan, H.N.1    El-Tawil, M.A.2
  • 19
    • 80052465750 scopus 로고    scopus 로고
    • Solution of Troesch's problem using He's polynomials
    • MR2815720
    • Mohyud-Din S. T., Solution of Troesch's problem using He's polynomials. Revista de la Unión Matemática Argentina 2011 52 1 143 148 MR2815720
    • (2011) Revista de la Unión Matemática Argentina , vol.52 , Issue.1 , pp. 143-148
    • Mohyud-Din, S.T.1
  • 21
    • 0038521511 scopus 로고    scopus 로고
    • Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation
    • 10.1016/S0096-3003(02)00345-4 MR1981688 ZBL1025.65042
    • Boyd J. P., Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation. Applied Mathematics and Computation 2003 143 2-3 189 200 10.1016/S0096-3003(02)00345-4 MR1981688 ZBL1025.65042
    • (2003) Applied Mathematics and Computation , vol.143 , Issue.2-3 , pp. 189-200
    • Boyd, J.P.1
  • 23
    • 20444478300 scopus 로고    scopus 로고
    • Adomian decomposition method for a reliable treatment of the Bratu-type equations
    • 10.1016/j.amc.2004.06.059 MR2151056 ZBL1073.65068
    • Wazwaz A.-M., Adomian decomposition method for a reliable treatment of the Bratu-type equations. Applied Mathematics and Computation 2005 166 3 652 663 10.1016/j.amc.2004.06.059 MR2151056 ZBL1073.65068
    • (2005) Applied Mathematics and Computation , vol.166 , Issue.3 , pp. 652-663
    • Wazwaz, A.-M.1
  • 24
    • 33646364314 scopus 로고    scopus 로고
    • An efficient method for solving Bratu equations
    • 10.1016/j.amc.2005.10.021 MR2232062 ZBL1093.65108
    • Syam M. I., Hamdan A., An efficient method for solving Bratu equations. Applied Mathematics and Computation 2006 176 2 704 713 10.1016/j.amc.2005.10.021 MR2232062 ZBL1093.65108
    • (2006) Applied Mathematics and Computation , vol.176 , Issue.2 , pp. 704-713
    • Syam, M.I.1    Hamdan, A.2
  • 25
    • 2342505312 scopus 로고    scopus 로고
    • Application of a Mickens finite-difference scheme to the cylindrical Bratu-Gelfand problem
    • 10.1002/num.10093 MR2046520 ZBL1048.65102
    • Buckmire R., Application of a Mickens finite-difference scheme to the cylindrical Bratu-Gelfand problem. Numerical Methods for Partial Differential Equations 2004 20 3 327 337 10.1002/num.10093 MR2046520 ZBL1048.65102
    • (2004) Numerical Methods for Partial Differential Equations , vol.20 , Issue.3 , pp. 327-337
    • Buckmire, R.1
  • 26
    • 0012166933 scopus 로고    scopus 로고
    • Numerical continuation and the Gelfand problem
    • 10.1016/S0096-3003(97)81660-8 MR1491706 ZBL0908.65094
    • McGough J. S., Numerical continuation and the Gelfand problem. Applied Mathematics and Computation 1998 89 1-3 225 239 10.1016/S0096-3003(97)81660-8 MR1491706 ZBL0908.65094
    • (1998) Applied Mathematics and Computation , vol.89 , Issue.1-3 , pp. 225-239
    • McGough, J.S.1
  • 27
    • 33745801140 scopus 로고    scopus 로고
    • From the fitting techniques to accurate schemes for the Liouville-Bratu-Gelfand problem
    • 10.1002/num.20116 MR2230270 ZBL1099.65098
    • Mounim A. S., de Dormale B. M., From the fitting techniques to accurate schemes for the Liouville-Bratu-Gelfand problem. Numerical Methods for Partial Differential Equations 2006 22 4 761 775 10.1002/num.20116 MR2230270 ZBL1099.65098
    • (2006) Numerical Methods for Partial Differential Equations , vol.22 , Issue.4 , pp. 761-775
    • Mounim, A.S.1    De Dormale, B.M.2
  • 28
    • 25844478165 scopus 로고    scopus 로고
    • An analytic approach to solve multiple solutions of a strongly nonlinear problem
    • 10.1016/j.amc.2004.09.066 MR2174686 ZBL1151.35354
    • Li S., Liao S.-J., An analytic approach to solve multiple solutions of a strongly nonlinear problem. Applied Mathematics and Computation 2005 169 2 854 865 10.1016/j.amc.2004.09.066 MR2174686 ZBL1151.35354
    • (2005) Applied Mathematics and Computation , vol.169 , Issue.2 , pp. 854-865
    • Li, S.1    Liao, S.-J.2
  • 29
    • 34848900880 scopus 로고    scopus 로고
    • A general approach to obtain series solutions of nonlinear differential equations
    • 10.1111/j.1467-9590.2007.00387.x MR2358643
    • Liao S., Tan Y., A general approach to obtain series solutions of nonlinear differential equations. Studies in Applied Mathematics 2007 119 4 297 354 10.1111/j.1467-9590.2007.00387.x MR2358643
    • (2007) Studies in Applied Mathematics , vol.119 , Issue.4 , pp. 297-354
    • Liao, S.1    Tan, Y.2
  • 30
    • 0141525039 scopus 로고    scopus 로고
    • A new approach to Bratu's problem
    • 10.1016/S0096-3003(02)00656-2 MR2007684 ZBL1032.65084
    • Khuri S. A., A new approach to Bratu's problem. Applied Mathematics and Computation 2004 147 1 131 136 10.1016/S0096-3003(02)00656-2 MR2007684 ZBL1032.65084
    • (2004) Applied Mathematics and Computation , vol.147 , Issue.1 , pp. 131-136
    • Khuri, S.A.1
  • 31
    • 77956262110 scopus 로고    scopus 로고
    • Non-polynomial spline method for solving Bratu's problem
    • 10.1016/j.cpc.2010.08.004 MR2718373 ZBL1219.65074
    • Jalilian R., Non-polynomial spline method for solving Bratu's problem. Computer Physics Communications 2010 181 11 1868 1872 10.1016/j.cpc.2010.08.004 MR2718373 ZBL1219.65074
    • (2010) Computer Physics Communications , vol.181 , Issue.11 , pp. 1868-1872
    • Jalilian, R.1
  • 33
    • 72149102881 scopus 로고    scopus 로고
    • Applying differential transformation method to the one-dimensional planar Bratu problem
    • MR2378565 ZBL1152.34008
    • Abdel-Halim Hassan I. H., Ertürk V. S., Applying differential transformation method to the one-dimensional planar Bratu problem. International Journal of Contemporary Mathematical Sciences 2007 2 29-32 1493 1504 MR2378565 ZBL1152.34008
    • (2007) International Journal of Contemporary Mathematical Sciences , vol.2 , Issue.29-32 , pp. 1493-1504
    • Abdel-Halim Hassan, I.H.1    Ertürk, V.S.2
  • 34
    • 77951077365 scopus 로고    scopus 로고
    • Numerical solution of Bratu-type equations by the variational iteration method
    • MR2663194 ZBL1196.65120
    • Batiha B., Numerical solution of Bratu-type equations by the variational iteration method. Hacettepe Journal of Mathematics and Statistics 2010 39 1 23 29 MR2663194 ZBL1196.65120
    • (2010) Hacettepe Journal of Mathematics and Statistics , vol.39 , Issue.1 , pp. 23-29
    • Batiha, B.1
  • 35
    • 79957917942 scopus 로고    scopus 로고
    • The Lie-group shooting method for solving the Bratu equation
    • 10.1016/j.cnsns.2011.03.033 MR2806735 ZBL1222.65067
    • Abbasbandy S., Hashemi M. S., Liu C.-S., The Lie-group shooting method for solving the Bratu equation. Communications in Nonlinear Science and Numerical Simulation 2011 16 11 4238 4249 10.1016/j.cnsns.2011.03.033 MR2806735 ZBL1222.65067
    • (2011) Communications in Nonlinear Science and Numerical Simulation , vol.16 , Issue.11 , pp. 4238-4249
    • Abbasbandy, S.1    Hashemi, M.S.2    Liu, C.-S.3
  • 37
    • 80855157357 scopus 로고    scopus 로고
    • A new operational matrix of derivative for Chebyshev wavelets and its applications in solving ordinary differential equations with non analytic solution
    • MR2837710 ZBL1250.65091
    • Hosseini S. Gh., Mohammadi F., A new operational matrix of derivative for Chebyshev wavelets and its applications in solving ordinary differential equations with non analytic solution. Applied Mathematical Sciences 2011 5 49-52 2537 2548 MR2837710 ZBL1250.65091
    • (2011) Applied Mathematical Sciences , vol.5 , Issue.49-52 , pp. 2537-2548
    • Hosseini, S.Gh.1    Mohammadi, F.2
  • 38
  • 39
    • 0003077036 scopus 로고
    • Philadelphia, Pa, USA SIAM CBMS-NSF Regional Conference Series in Applied Mathematics 10.1137/1.9781611970104 MR1162107
    • Daubechies I., Ten Lectures on Wavelets 1992 61 Philadelphia, Pa, USA SIAM xx+357 CBMS-NSF Regional Conference Series in Applied Mathematics 10.1137/1.9781611970104 MR1162107
    • (1992) Ten Lectures on Wavelets , vol.61
    • Daubechies, I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.