Solving integral and differential equations by the aid of non-uniform Haar wavelets

Lepik, Ülo

doi:10.1016/j.amc.2007.08.036

Cited by 41 publications

(31 citation statements)

References 8 publications

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“…In this paper only ordinary differential equations were considered, but the same approach is applicable also for stiff partial differential equations. We recommend to consult the paper [15] in which the Burgers equation was solved.…”

Section: Discussionmentioning

confidence: 99%

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Haar Wavelet Method for Solving Stiff Differential Equations

Lepik

2009

Mathematical Modelling and Analysis

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Section: Discussionmentioning

confidence: 99%

“…There are some complementary possibilities to raise the stability of the solution. First, we could use the wavelets with a variable step size (see, [15], especially the example in Section 5). If we develop Ü. Lepik into the Haar series the highest derivative y (n) , then it is not continuous: this fact may also cause some instabilities.…”

Section: Discussionmentioning

confidence: 99%

Haar Wavelet Method for Solving Stiff Differential Equations

Lepik

2009

Mathematical Modelling and Analysis

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“…In [8] Maleknejad used Legendre wavelets, Xufeng Shang in [11] applied the Legendre multi wavelets. In [6] and [5] Lepik and Gu proposed non-uniform Haar wavelets and Trigonometric Hermit wavelets too. Recently, wavelets basis are applied in order to solve various kinds of integral equations [1,2,8].…”

Section: The Journal Of Mathematics and Computer Sciencementioning

confidence: 99%

Numerical Solution Of Fredholm And Volterra Integral Equations Of The First Kind Using Wavelets Bases

Bahmanpour¹,

Araghi²

2012

J. Math. Computer Sci.

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The Fredholm and Volterra types of integral equations are appeared in many engineering fields. In this paper, we suggest a method for solving Fredholm and Volterra integral equations of the first kind based on the wavelet bases. The Haar, continuous Legendre, CAS, Chebyshev wavelets of the first kind (CFK) and of the second kind (CSK) are used on [0,1] and are utilized as a basis in Galerkin or collocation method to approximate the solution of the integral equations. In this case, the integral equation converts to the system of linear equations. Then, in some examples the mentioned wavelets are compared with each other.

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“…It allows also for detection of a birth/death of a frequency and time of its occurrence/vanishment. Although there exist different types of wavelets [42,43], the Morlet wavelet is the most suitable for our purpose. The analysis of advantages and disadvantages of different wavelet types to be employed in the study of shells can be found in reference [44].…”

Section: Dynamics Of a Contact Interactionmentioning

confidence: 99%

Contact interaction of two rectangular plates made from different materials with an account of physical nonlinearity

et al. 2017

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A mathematical model of a contact interaction between two plates made from materials with different elasticity modulus is derived taking into account physical and design nonlinearities. In order to study the stress-strain state of this complex mechanical structure, the method of variational iteration has been employed allowing for reduction of partial differential equations to ordinary differential equations (ODEs). The theorem regarding convergence of this method is formulated for the class of similar-like problems. The convergence of the proposed iterational procedure used for obtaining a solution to contact problems of two plates is proved. In the studied case, the physical nonlinearity is introduced with the help of variable parameters associated with plate stiffness. The work is supplemented with a few numerical examples. Both

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Solving integral and differential equations by the aid of non-uniform Haar wavelets

Cited by 41 publications

References 8 publications

Haar Wavelet Method for Solving Stiff Differential Equations

Haar Wavelet Method for Solving Stiff Differential Equations

Numerical Solution Of Fredholm And Volterra Integral Equations Of The First Kind Using Wavelets Bases

Contact interaction of two rectangular plates made from different materials with an account of physical nonlinearity

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