Related papers: Taylor Series for Adomian Decomposition Method
In [7], a new iterative method for solving linear system of equations was presented which can be considered as a modification of the Gauss-Seidel method. Then in [4] a different approach, say 2D-DSPM, and more effective one was introduced.…
In the present work, we use the Adomian Decomposition method to find the approximate solution for some cases of the Newell whitehead segel nonlinear differential equation which was solved previously with exact solution by the Homotopy…
Solutions to most nonlinear ordinary differential equations (ODEs) rely on numerical solvers, but this gives little insight into the nature of the trajectories and is relatively expensive to compute. In this paper, we derive analytic…
We contribute to the method of trigonometric series for solving differential equations of certain non linear oscillators. Key Words: series power solution, trigonometric series.
The Adomian decomposition method (ADM) is a universal approach to solving governing equations in various engineering and technological applications. The applicability of the ADM is almost limitless due to its universal applicability, but…
The representation of the solution of some Backward Stochastic Differential Equation as an infinite series is obtained. Some exactly solvable examples are considered.
We introduce the method of path-sums which is a tool for exactly evaluating a function of a discrete matrix with possibly non-commuting entries, based on the closed-form resummation of infinite families of terms in the corresponding Taylor…
We use elliptic Taylor series expansions and interpolation to deduce a number of summations for elliptic hypergeometric series. We extend to the well-poised elliptic case results that in the $q$-case have previously been obtained by Cooper…
A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bi-linear and commutative mapping on the solution space, is studied. This family of PDE's contains…
In this paper, we introduce an algorithm that provides approximate solutions to semi-linear ordinary differential equations with highly oscillatory solutions, which, after an appropriate change of variables, can be rewritten as…
The development of functions of real variables in Taylor and Frobenius series (whole series which are formed in nonorthogonal, nonperiodic bases), in sinusoidal Fourier series (bases of orthogonal, periodic functions), in series of special…
In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion. In particular, spaces of generalized functions are constructed that contain generalized solutions to all systems of continuous,…
We give new algorithms based on the sum-of-squares method for tensor decomposition. Our results improve the best known running times from quasi-polynomial to polynomial for several problems, including decomposing random overcomplete…
Power series in which the summand satisfies a linear recurrence relation with polynomial coefficients are shown to be the solution of a linear differential or algebraic equation. Solving the associated differential or algebraic equation…
The aim of this paper is to present an efficient numerical procedure to approximate the generalized Abel's integral equations of the first and second kinds. For this reason, the Taylor polynomials and the collocation method are applied.…
It was shown in 1994, in Oberguggenberger & Rosinger, that very large classes of nonlinear PDEs have solutions which can be assimilated with usual measurable functions on the Euclidean domains of definition of the respective equations. In…
We present methods for constructing Taylor series surrogate models for covariance preconditioned high dimensional mappings that depend implicitly on the solution of a system of nonlinear equations, e.g., the solution of a partial…
Pointwise-supported generalized wavelets are introduced, based on Dirac, doublet and further derivatives of delta. A generalized biorthogonal analysis leads to standard Taylor series and new Dual-Taylor series that may be interpreted as…
In this article, we construct a representation formula for stochastic B-series evaluated in a B-series. This formula is used to give for the first time the order conditions of implicit Taylor methods in terms of rooted trees. Finally, as an…
The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…