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Volumn 37, Issue 1-4 SPEC. ISS., 2004, Pages 311-323

An efficient approach to the numerical verification for solutions of elliptic differential equations

Author keywords

elliptic equations; fixed point theorem; numerical verification

Indexed keywords


EID: 10044260069     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:NUMA.0000049477.75366.94     Document Type: Conference Paper
Times cited : (21)

References (13)
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    • Nakao, M.T.1
  • 5
    • 38249013605 scopus 로고
    • A numerical verification method for the existence of weak solutions for nonlinear boundary value problems
    • M.T. Nakao, A numerical verification method for the existence of weak solutions for nonlinear boundary value problems, J. Math. Anal. Appl. 164 (1992), 489-507.
    • (1992) J. Math. Anal. Appl. , vol.164 , pp. 489-507
    • Nakao, M.T.1
  • 6
    • 0035326665 scopus 로고    scopus 로고
    • Numerical verification methods for solutions of ordinary and partial differential equations
    • M.T. Nakao, Numerical verification methods for solutions of ordinary and partial differential equations, Numer. Funct. Anal. Optim. 22 (2001) 321-356.
    • (2001) Numer. Funct. Anal. Optim. , vol.22 , pp. 321-356
    • Nakao, M.T.1
  • 8
    • 0035587860 scopus 로고    scopus 로고
    • Computer-assisted enclosure methods for elliptic differential equations
    • M. Plum, Computer-assisted enclosure methods for elliptic differential equations, Linear Algebra Appl. 324 (2001) 147-187.
    • (2001) Linear Algebra Appl. , vol.324 , pp. 147-187
    • Plum, M.1
  • 9
    • 0026761994 scopus 로고
    • On the solution of interval linear systems
    • S.M. Rump, On the solution of interval linear systems, Computing 47 (1992) 337-353.
    • (1992) Computing , vol.47 , pp. 337-353
    • Rump, S.M.1
  • 10
    • 33746928018 scopus 로고
    • Verification methods for dense and sparse systems of equations
    • ed. J. Herzberger Elsevier Science/North-Holland, Amsterdam
    • S.M. Rump, Verification methods for dense and sparse systems of equations, in: Topics in Validated Computations, ed. J. Herzberger (Elsevier Science/North-Holland, Amsterdam, 1994) pp. 63-135.
    • (1994) Topics in Validated Computations , pp. 63-135
    • Rump, S.M.1
  • 12
    • 0036772161 scopus 로고    scopus 로고
    • Verified numerical computations for multiple and nearly multiple eigenvalues of elliptic operators
    • K. Toyonaga, M.T. Nakao and Y. Watanabe, Verified numerical computations for multiple and nearly multiple eigenvalues of elliptic operators, J. Comput. Appl. Math. 147 (2002) 175-190.
    • (2002) J. Comput. Appl. Math. , vol.147 , pp. 175-190
    • Toyonaga, K.1    Nakao, M.T.2    Watanabe, Y.3
  • 13
    • 10044237618 scopus 로고    scopus 로고
    • A numerical verification of nontrivial solutions for the heat convection problem
    • Y. Watanabe, N. Yamamoto, M.T. Nakao and T. Nishida, A numerical verification of nontrivial solutions for the heat convection problem, J. Math. Fluid Mech. 6 (2004) 1-20.
    • (2004) J. Math. Fluid Mech. , vol.6 , pp. 1-20
    • Watanabe, Y.1    Yamamoto, N.2    Nakao, M.T.3    Nishida, T.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.