Efficient Computation of Laplace Residual Power Series with Explicit Coefficient Formulas

Pisamai Kittipoom

Home/Archive/arXiv

arXiv · 2407.04705

Efficient Computation of Laplace Residual Power Series with Explicit Coefficient Formulas

Pisamai Kittipoom

View original source ↗Read source document ↗Export metadata ↓

Abstract

The Residual Power Series Method (RPSM) provides a powerful framework for solving fractional differential equations. However, a significant computational bottleneck arises from the necessity of calculating the fractional derivatives of the residual function within the coefficient determination process. The Laplace Residual Power Series Method (LRPSM) partially addresses this by employing the Laplace transform. However, it introduces additional complexities and requires the computation of the residual error function at each iteration. This work presents a novel approach that directly derives explicit formulas for the coefficients, Bypassing the need for iterative residual error function calculations. This advancement significantly enhances the computational efficiency of the method compared to both RPS method and LRPS method.

Explore related subjects

math.GM

Keep this discovery

BibTeX RIS

Pisamai Kittipoom. 2024-05-03. Efficient Computation of Laplace Residual Power Series with Explicit Coefficient Formulas. https://arxiv.org/abs/2407.04705

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Average Chord Lengths in a Triangle

Let $P$ be a point inside a triangle $T$. We consider the average length of the chords of $T$ through $P$, where the direction of the chord is chosen uniformly. An elementary formula is obtained in terms of the distances from $P$ to the sides and vertices of the triangle. Several classical triangle centers give especially simple specializations. For example, if $I$ is the incenter, then \[ M_T(I)=\frac{2r}{\pi} \log\left(\cot\frac A4\cot\frac B4\cot\frac C4\right). \] Our main result is the sharp inequality \[ M_T(P)\le \frac{p}{\pi\sqrt3}\log(2+\sqrt3), \] valid simultaneously for every triangle of perimeter $p$ and every interior point $P$. Thus, among all such pairs $(T,P)$, the largest possible average chord length occurs only when $T$ is equilateral and $P$ is its center. The proof is an elementary symmetrization argument. We close with brief remarks relating the problem to the radial center of a convex body, the electrostatic potential center of a triangle, and dual quermassintegrals.

math.GM↗

arXiv2026

The decrease in sectional curvature of the Fisher--Rao manifold of beta distributions

In the paper, the author develops a general convexity lemma and applies it to demonstrate the monotonic decrease of a function involving polygamma functions, arising from the sectional curvature of the Fisher--Rao manifold of beta distributions.

math.GM↗

arXiv2026

A Proof of Liu's Conjecture on the Fundamental Triangle Inequality

Let $a,b,c$ be the side lengths of a triangle, and let $R$ and $r$ denote its circumradius and inradius, respectively. We prove a conjecture of Liu stating that \[\sum_{\mathrm{cyc}} \left(\frac{a(b+c-a)}{bc}\right)^k \geq 2+\left(\frac{2r}{R}\right)^k,~~k>1, \] with the reverse inequality for $0<k<1$. The proof reduces the problem to three positive variables with fixed sum and product. We also determine the equality cases.

math.GM↗