zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Intuitive approach to the approximate analytical solution for the Blasius problem. (English) Zbl 1183.65098
Summary: For the Blasius problem, we propose an approximate analytical solution in the form of a logarithm of the hyperbolic cosine function which satisfies the given boundary conditions and some known properties of the exact solution. Furthermore, adding some hyperbolic tangent functions to this solution, we obtain much more accurate approximate solution with the relative error less than 0.16% over the whole region. The superiority of the proposed solutions is shown by comparison with the existing approximate analytical solution.
MSC:
65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
References:
[1]Boyd, J. P.: The Blasius function: computations before computers, the value of tricks, undergraduate projects, and open research problems, SIAM rev. 50, 791-804 (2008) · Zbl 1152.76024 · doi:10.1137/070681594
[2]Boyd, J. P.: Padé approximant algorithm for solving nonlinear ODE boundary value problems on an unbounded domain, Comput. phys. 11, 299-303 (1997)
[3]Boyd, J. P.: The Blasius equation in the complex plane, J. exp. Math. 8, 381-394 (1999) · Zbl 0980.34053
[4]Adomian, G.: A review of the decomposition method in applied mathematics, J. math. Anal. appl. 135, 501-544 (1988) · Zbl 0671.34053 · doi:10.1016/0022-247X(88)90170-9
[5]Adomian, G.: Solution of the Thomas – Fermi equation, Appl. math. Lett. 11, 131-133 (1998) · Zbl 0947.34501 · doi:10.1016/S0893-9659(98)00046-9
[6]He, J. H.: Approximate analytical solution of Blasius equation, Commun. nonlinear sci. Numer. simul. 3, 260-263 (1998) · Zbl 0918.34016 · doi:10.1016/S1007-5704(98)90046-6
[7]He, J. H.: A review on some new recently developed nonlinear analytical techniques, Int. J. Nonlinear sci. Numer. simul. 140, 217-222 (2000)
[8]He, J. H.: A simple perturbation approach to Blasius equation, Appl. math. Comput. 140, 217-222 (2003) · Zbl 1028.65085 · doi:10.1016/S0096-3003(02)00189-3
[9]Lin, J.: An new approximate iteration solution of Blasius equation, Commun. nonlinear sci. Numer. simul. 4, 91-94 (1999) · Zbl 0928.34012 · doi:10.1016/S1007-5704(99)90017-5
[10]Parlange, J.; Braddock, R. D.; Sander, G.: Analytical approximations to the solution of the Blasius equation, Acta mech. 38, 119-125 (1981) · Zbl 0463.76042 · doi:10.1007/BF01351467
[11]Wazwaz, A. M.: The variational iteration method for solving two forms of Blasius equation on a half-infinite domain, Appl. math. Comput. 188, 485-491 (2007) · Zbl 1114.76055 · doi:10.1016/j.amc.2006.10.009
[12]Allan, F. M.; Syam, M. I.: On the analytic solution of the nonhomogeneous Blasius problem, J. comput. Appl. math. 182, 362-371 (2005) · Zbl 1071.65108 · doi:10.1016/j.cam.2004.12.017
[13]Datta, B. K.: Analytic solution for the Blasius equation, Indian J. Pure appl. Math. 34, 237-240 (2003) · Zbl 1054.34011
[14]Liao, S. J.: A uniformly valid analytic solution of 2-D viscous flow over a semi-infinite flat plate, J. fluid mech. 385, 101-128 (1999) · Zbl 0931.76017 · doi:10.1017/S0022112099004292
[15]Liao, S. J.: An explicit, totally analytic approximate solution for Blasius viscous flow problems, Int. J. Nonlinear mech. 34, 759-778 (1999)
[16]Howarth, L.: On the solution of the laminar boundary equations, Proc. roy. Soc. London, ser. A 164, 547-579 (1938) · Zbl 64.1452.01 · doi:10.1098/rspa.1938.0037