This paper first introduces Legendre wavelet bases and derives their rich properties. Then these properties are applied to estimation of approximation error upper bounded in spaces and by norms and &...This paper first introduces Legendre wavelet bases and derives their rich properties. Then these properties are applied to estimation of approximation error upper bounded in spaces and by norms and , respectively. These estimate results are valuable to solve integral-differential equations by Legendre wavelet method.展开更多
In this paper,we develop an accurate and efficient Legendre wavelets method for numerical solution of the well known time-fractional telegraph equation.In the proposed method we have employed both of the operational m...In this paper,we develop an accurate and efficient Legendre wavelets method for numerical solution of the well known time-fractional telegraph equation.In the proposed method we have employed both of the operational matrices of fractional integration and differentiation to get numerical solution of the time-telegraph equation.The power of this manageable method is confirmed.Moreover the use of Legendre wavelet is found to be accurate,simple and fast.展开更多
In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] a...In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other.展开更多
The present study deals with the introduction of an alteration in Legendre wavelets method by availing of the Picard iteration method for system of differential equations and named it Legendre wavelet-Picard method （...The present study deals with the introduction of an alteration in Legendre wavelets method by availing of the Picard iteration method for system of differential equations and named it Legendre wavelet-Picard method （LWPM）. Convergence of the proposed method is also discussed. In order to check the competence of the proposed method, basic enzyme kinetics is considered. Systems of nonlinear ordinary differential equations are formed from the considered enzyme-substrate reaction. The results obtained by the proposed LWPM are compared with the numerical results obtained from Runge-Kutta method of order four （RK-4）. Numerical results and those obtained by LWPM are in excellent conformance, which would be explained by the help of table and figures. The proposed method is easy and simple to implement as compared to the other existing analytical methods used for solving systems of differential equations arising in biology, physics and engineering.展开更多
文摘This paper first introduces Legendre wavelet bases and derives their rich properties. Then these properties are applied to estimation of approximation error upper bounded in spaces and by norms and , respectively. These estimate results are valuable to solve integral-differential equations by Legendre wavelet method.
文摘In this paper,we develop an accurate and efficient Legendre wavelets method for numerical solution of the well known time-fractional telegraph equation.In the proposed method we have employed both of the operational matrices of fractional integration and differentiation to get numerical solution of the time-telegraph equation.The power of this manageable method is confirmed.Moreover the use of Legendre wavelet is found to be accurate,simple and fast.
文摘In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other.
文摘The present study deals with the introduction of an alteration in Legendre wavelets method by availing of the Picard iteration method for system of differential equations and named it Legendre wavelet-Picard method （LWPM）. Convergence of the proposed method is also discussed. In order to check the competence of the proposed method, basic enzyme kinetics is considered. Systems of nonlinear ordinary differential equations are formed from the considered enzyme-substrate reaction. The results obtained by the proposed LWPM are compared with the numerical results obtained from Runge-Kutta method of order four （RK-4）. Numerical results and those obtained by LWPM are in excellent conformance, which would be explained by the help of table and figures. The proposed method is easy and simple to implement as compared to the other existing analytical methods used for solving systems of differential equations arising in biology, physics and engineering.
