Differential equations can be solved using several approaches and one such approach is the use of wavelets. When using wavelets the coefficient is very crucial to finding an appropriate solution.
Hi,
Since there is discontinuouty in Haar wavelets they are not directly used for solving odes or pdes. Instead, integrals of Haar wavelets are utilized to solve odes or pdes. To do so, firstly highest order derivative of unknown function is expressed in terms of Haar wavelets, then by using the integrals of Haar wavelets the unknown function itself is found. Next, by plugging the expressions obtained for unknown function and its derivatives into given differential equation a linear or nonlinear algebraic system of equations is acquired via choosing collocation points. Finally solving the system of equations the wavelet coefficients can be found. For more details you can consult to series of papers from U.Lepik, or take a look at to my researchs.
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