In Section 3, we introduce and analyze the Legendre collocation scheme to approximate the solution of (1.1).
This implies that some derivatives of the exact solutions of (1.1) have a singularity near the end point t = 0+ with the asymptotic behavior (2.2), (2.3), and thereby a direct application of the Legendre collocation method for the numerical solution of (1.1) may lead to results with low accuracy.
Section 2 provides the necessary mathematical background concerning the Gaussian radial basis function and also the fundamental idea of collocation mesh-free schemes in general.
Under the context of collocation schemes, this relation is linked to the Euclidean distance function, [[parallel]x[parallel].sub.2], via the following multivariate function:
This pioneering study is based on the collocation Trefftz method and provides a promising solution which integrates the T-Trefftz method and F-Trefftz method for constructing its basis function using one of the particular solutions which satisfies the governing equation and allows many source points outside the domain of interest.
The evaluation of coefficients may be obtained by solving the unknown coefficients in the linear combination of the solutions which are accomplished by collocation imposing the boundary condition at a finite number of points.
Based on a synthesis of the theoretical tools of CPT (i.e., collocation, semantic prosody, and subtext), Milojkovic analyzes the logical construction of literary worlds as well as a hitherto uncharted domain in corpus stylistics: authorial intention, that is, whether the author sincerely means what he or she writes.
It is a consensus that the ways one defines collocation influences our understanding of semantic prosody.
in beginner learner writing: A longitudinal study.
3) To what extent can an even wider context and the extralinguistic context reveal the equivalent extended term-embedding collocation
in the target text if it turns out downright for the corpus data to do so?
In the present paper we construct two high-order collocation
type methods for the numerical solution of the fractional differential equation with non-local boundary values in the following form:
It combines meshfree method known as solution structure method, atomic basis functions (ABFs) and a collocation
In a numerical point of view, the methods that are based on the operational matrices of differentiation may be divided into the collocation
and Tau matrix methods.
If a mesh interval has met the accuracy tolerance, that is, [e.sup.(k).sub.max] [less than or equal to] [epsilon], where [epsilon] is the desired relative tolerance, then mesh size is reduced by decrease of the number of collocation
points or merging adjacent mesh intervals; otherwise the mesh size needs to be modified by increasing points or dividing that mesh interval into several subintervals.
Finally, the term collocation
was coined by Firth to refer to the common co-occurrence of two or more words (cf.