Sideways heat equation and wavelets

Regińska, Teresa

doi:10.1016/0377-0427(95)00073-9

Cited by 56 publications

(26 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Fu et al give a priori and a posteriori Fourier regularization method to solve this problem, respectively. In the present paper we will adopt the Meyer wavelet regularization method to deal with this ill-posed problem, which is motivated by some earlier works [18] for the sideways heat equation. The essence of the Meyer wavelet regularization method is just to filter the high frequencies (which cause blow up) of the noisy data.…”

Section: )mentioning

confidence: 99%

“…Moreover, solving many ill-posed problems can lead to the numerical pseudo-differential operator, such as numerical differentiation [8], the inverse heat conduction problem [15,18,19] , the Cauchy problem of the Laplace equation [16], the backward heat conduction problem and so on [17], the details we can refer to [7,9]. Therefore the study of regularization…”

Section: )mentioning

confidence: 99%

See 1 more Smart Citation

Wavelets and numerical pseudodifferential operator

Cheng

2016

Applied Mathematical Modelling

View full text Add to dashboard Cite

Highlights• The NΨDO present a new general framework for solving the ill-posed problems.• The results for combination of the ΨDO and ill-posed problem is still very sparse.• Using the Meyer wavelet method, the order optimal error estimates are given.• Theoretical evaluation and numerical test validate the effectiveness of the method. AbstractCalculating the value for the pseudodifferential operator with unbounded symbol is an ill-posed problem. In the present paper we adopt a wavelet regularization method to solve this problem, error estimates of Hölder type between the regularized values and the exact values are derived. Applications of the general theory scheme and numerical test to the concrete problems are presented.

show abstract

Section: )mentioning

confidence: 99%

Section: )mentioning

confidence: 99%

Wavelets and numerical pseudodifferential operator

Cheng

2016

Applied Mathematical Modelling

View full text Add to dashboard Cite

show abstract

“…In the one-dimensional setting, assuming that the body is large, this problem occasionally leads to the following sideways parabolic equation of nondivergenee type in the quarter plane [3][4][5][6]: We want to know the solution u(x, t) for 0 < x < 1. IHCP are mainly devoted to the standard sideways heat equation [2,[7][8][9][10][11][12][13] In [14], the authors have considered a noncharacteristic Cauchy problem of a general parabolic equation ut = a(x)uxx + b(x)u~ + e(x)u, x e (0, 0, t • I,…”

Section: Introductionmentioning

confidence: 99%

Two regularization methods and the order optimal error estimates for a sideways parabolic equation

Xiong

et al. 2005

Computers & Mathematics with Applications

View full text Add to dashboard Cite

In this paper, we consider an inverse heat conduction problem which appears in some applied subjects. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. A Tikhonov type's regularization method and a Fourier regularization method are applied to formulate regularized solutions which are stably convergent to the exact ones with order optimal error estimates. A numerical example shows that the computational effect of these methods are all satisfactory. ~)

show abstract

“…This problem is called an inverse heat conduction problem (IHCP). In a one-dimensional setting, assuming that the body is large, the following model problem or the standard sideways heat equation: has been discussed by many authors [4,6,7,10,16,18,19,20]. But when a fluid is flowing through the solid, for example, a gas is travelling from the rear surface, there must be a convection term in heat conduction equation [1,17].…”

Section: Introductionmentioning

confidence: 99%