we present here the numerical solution of damped forced oscillator problem using haar wavelet and compare the numerical results obtained with some well-known numerical methods such as runge-kutta fourth order classical and taylor series methods. numerical results show that the present haar wavelet method gives more accurate approximations than above said numerical methods.

A Taylor matrix method is developed to find an approximate solution of the most general linear Fredholm integrodifferential-difference equations with variable coefficients under the mixed conditions in terms of Taylor polynomials. This method transforms the given general linear Fredholm integrodifferential-difference equations and the mixed conditions to matrix equations with unknown Taylor coe...

This paper is one of a series underpinning the authors’ DAETS code for solving DAE initial value problems by Taylor series expansion. First, building on the second author’s structural analysis of DAEs (BIT 41 (2001) 364–394), it describes and justifies the method used in DAETS to compute Taylor coefficients (TCs) using automatic differentiation. The DAE may be fully implicit, nonlinear, and con...

In this paper a computational algorithm for nonlinear balanced realization and model reduction based on Taylor series expansion is proposed. This algorithm requires recursive computations with respect to the order of the Taylor series in which we need to solve linear equations with unknown parameters in each step. Furthermore, the proposed method is applied to a double pendulum system. Some num...

Achieving improved order of accuracy for a hydrodynamic numerical method is a continuing quest. The discrete approximate solution error, in general, can be expressed as a truncation of a Taylor series expansion. This paper presents a weak statement perturbation methodology retaining block-tridiagonal forms that can reduce, or annihilate in special cases, the Taylor series truncation error to hi...

The Taylor series expansion of continuous functions has shown in many fields to be an extremely powerful tool to study the characteristics of such functions. This paper illustrates the power of the Taylor series expansion of multilayer feedforward neural networks. The paper shows how these expansions can be used to investigate positions of decision boundaries, to develop active learning strateg...

Let M and N be smooth manifolds without boundary. Immersion theory suggests that an understanding of the space of smooth embeddings emb(M,N) should come from an analysis of the cofunctor V 7→ emb(V,N) from the poset O of open subsets of M to spaces. We therefore abstract some of the properties of this cofunctor, and develop a suitable calculus of such cofunctors, Goodwillie style, with Taylor s...

The Taylor series method is one of the earliest analytic-numeric algorithms for approximate solution of initial value problems for ordinary differential equations. The main idea of the rehabilitation of this algorithms is based on the approximate calculation of higher derivatives using well-known finite-difference technique for the partial differential equations. The approximate solution is giv...

In recent years, microcontrollers have been used in many areas. Implementation of a circuit by using several discrete analog and digital devices can be done using only one microcontroller. However, industrial microcontrollers have limited resources to implement complex mathematical functions, such as Taylor series. In this work, implementation of Taylor series on a PIC microcontroller is given....