[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Introduction To Stochastic Calculus With Applications

Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations

Solving a nonlinear fractional differential equation using Chebyshev wavelets

In the numerical analysis, Wavelets play an important role in the solution of differential equations. In this paper, we apply the Haar wavelet collocation method (HWCM) for solving multi-term fractional differential equations (FDEs) using the fractional order operational matrix of integration. The present study is illustrated by exploring different kinds of FDEs that gives the approximate solution is good agreement with the exact solution than the Haar wavelet-based method presented by Li and Zhao (Appl Math Comput 216:2276–2285, 2010) and other methods by Ford and Connolly (J Comput Appl Math 229:382–391, 2009), El-Sayed et al. (Appl Math Comput 60:788–797, 2010). The error will be reduced by increasing the number of collocation points, which has been justified through the examples.

An efficient Haar wavelet collocation method for the numerical solution of multi-term fractional differential equations

In this paper, new operational matrix of integration is generated by using Hermite wavelets. By aid of these matrices, Hermite wavelets operational matrix method (HWOMM) is developed for second ordered nonlinear singular initial value problems. Properties of Hermite wavelets are used to convert the differential equations into system of algebraic equations which can be efficiently solved by suitable solvers. Illustrative numerical problems are considered to demonstrate the applicability of the proposed technique and those results are comparing favourably with the exact solutions and errors.

Hermite wavelets operational matrix of integration for the numerical solution of nonlinear singular initial value problems

Theoretical study on continuous polynomial wavelet bases through wavelet series collocation method for nonlinear Lane–Emden type equations

Computation of eigenvalues and solutions of regular Sturm-Liouville problems using Haar wavelets

https://www.tandfonline.com/doi/pdf/10.1080/16583655.2018.1515324

S. C. Shiralashetti

Papers

An efficient Haar wavelet collocation method for the numerical solution of multi-term fractional differential equations

Hermite wavelets operational matrix of integration for the numerical solution of nonlinear singular initial value problems

Theoretical study on continuous polynomial wavelet bases through wavelet series collocation method for nonlinear Lane–Emden type equations

Computation of eigenvalues and solutions of regular Sturm-Liouville problems using Haar wavelets

Laguerre wavelets collocation method for the numerical solution of the Benjamina–Bona–Mohany equations