The explicit form for the orthonormal periodic trigonometric spline wavelet is given. We also give the decomposition and reconstruction equations.Each of the two equations involves onlytwo terms. We prove that the fam...The explicit form for the orthonormal periodic trigonometric spline wavelet is given. We also give the decomposition and reconstruction equations.Each of the two equations involves onlytwo terms. We prove that the family of periodic trigonometric spline wavelets is dense in L2([0,2π]).展开更多
We develop a new sixth-order accurate numerical scheme for the solution of two point boundary value problems.The scheme uses nonpolynomial spline basis and high order finite difference approximations.With the help of ...We develop a new sixth-order accurate numerical scheme for the solution of two point boundary value problems.The scheme uses nonpolynomial spline basis and high order finite difference approximations.With the help of spline functions,we derive consistency conditions and it is used to derive high order discretizations of the first derivative.The resulting difference schemes are solved by the standard Newton’s method and have very small computing time.The new method is analyzed for its convergence and the efficiency of the proposed scheme is illustrated by convection-diffusion problem and nonlinear Lotka–Volterra equation.The order of convergence and maximum absolute errors are computed to present the utility of the new scheme.展开更多
基金This work is pastially supported by NNSFCthe Foundation of Zhongshan University Advanced Reseasch Centre
文摘The explicit form for the orthonormal periodic trigonometric spline wavelet is given. We also give the decomposition and reconstruction equations.Each of the two equations involves onlytwo terms. We prove that the family of periodic trigonometric spline wavelets is dense in L2([0,2π]).
文摘We develop a new sixth-order accurate numerical scheme for the solution of two point boundary value problems.The scheme uses nonpolynomial spline basis and high order finite difference approximations.With the help of spline functions,we derive consistency conditions and it is used to derive high order discretizations of the first derivative.The resulting difference schemes are solved by the standard Newton’s method and have very small computing time.The new method is analyzed for its convergence and the efficiency of the proposed scheme is illustrated by convection-diffusion problem and nonlinear Lotka–Volterra equation.The order of convergence and maximum absolute errors are computed to present the utility of the new scheme.
