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Solutions for the earth return mutual impedance play an important role in analyzing couplings of multi-conductor systems. Generally, the mutual impedance is approximated by Pollaczek integrals. The purpose of this paper is devising fast algorithms for calculation of this kind of improper integrals and its applications.

According to singular points, the Pollaczek integral is divided into two parts: the finite integral and the infinite integral. The finite part is computed by combining an efficient Levin method, which is implemented with a Chebyshev differential matrix. By transforming the integration path, the tail integral is calculated with help of a transformed Clenshaw–Curtis quadrature rule.

Numerical tests show that this new method is robust to high oscillation and nearly singularities. Thus, it is suitable for evaluating Pollaczek integrals. Furthermore, compared with existing method, the presented algorithm gives high-order approaches for the earth return mutual impedance between conductors over a multilayered soil with wide ranges of parameters.

An efficient truncation strategy is proposed to accelerate numerical calculation of Pollaczek integral. Compared with existing algorithms, this method is easier to be applied to computation of similar improper integrals, such as Sommerfeld integral.

This paper sets out to introduce a numerical method to obtain solutions of Fredholm‐Volterra type linear integral equations.

The flow of the paper uses well‐known formulations, which are referenced at the end, and tries to construct a new approach for the numerical solutions of Fredholm‐Volterra type linear equations.

The approach and obtained method exhibit consummate efficiency in the numerical approximation to the solution. This fact is illustrated by means of examples and results are provided in tabular formats.

Although the method is suitable for linear equations, it may be possible to extend the approach to nonlinear, even to singular, equations which are the future objectives.

In many areas of mathematics, mathematical physics and engineering, integral equations arise and most of these equations are only solvable in terms of numerical methods. It is believed that the method is applicable to many problems in these areas such as loads in elastic plates, contact problems of two surfaces, and similar.

The paper is original in its contents, extends the available work on numerical methods in the solution of certain problems, and will prove useful in real‐life problems.

The earth-return mutual impedances between underground and overhead conductors can be expressed by Pollaczek integrals. Many efforts have been exerted to calculating this kind of integrals. However, most of numerical methods turn out to be time-consuming as integrands become highly oscillatory and strongly singular. Therefore, efficient algorithms should be devised. The paper aims to discuss these issues.

The paper separates the singularity from the whole integral and couple with the singularity and oscillation, respectively. A sinh transformation is applied for the finite part and complex integration method is used to calculate the tail.

Numerical experiments show that the given method shares the property that the stronger the singularity and the higher the oscillation, the better the accuracy of the calculation.

The sinh transformation is first proposed to calculate Pollaczek integrals. This efficient algorithm can be used to evaluate mutual impedances between conductors. Also, it provides a new aspect of the research on fast calculation of Pollaczek integrals and Sommerfeld integrals.

Fiber networks represent a vast class of materials, which can be modeled by representing its microstructure using one-dimensional fiber embedded in three-dimensional space. Investigating the statics, dynamics and thermodynamics of such structures from computational first principles requires the efficient estimation of cohesive-repulsive energies and forces between interacting fiber segments. This study offers a fast, efficient and effective computational methodology to estimate such interactions which can be coupled with Hamiltonian mechanics to simulate the behavior of fibrous systems.

This method preserves the uniformly continuous distribution of particles on the line segments and utilizes adaptive numerical integration of relevant distance-distribution functions to estimate the effective interaction energy and forces.

This method is found to be cheaper to compute and more accurate than the corresponding discrete scheme. This scheme is also versatile in the sense that any pair-wise interaction model can be used.

The scheme depends on the availability of a suitable pair-interaction potential, such as a Lennard-Jones potential or Morse potential. Additionally, it can only be used for systems which are purely fibrous in nature. For example, fiber composites with a non-fibrous matrix are not addressed.

Paper, woven and hair can be represented as purely fibrous at some relevant length scales and are thus excellent candidate systems for this scheme.

This paper presents a novel method which allows rapid and accurate implementation of an otherwise computationally expensive process.

The main purpose of this paper is to implement the piecewise spectral-variational iteration method (PSVIM) to solve the nonlinear Lane-Emden equations arising in mathematical physics and astrophysics.

This method is based on a combination of Chebyshev interpolation and standard variational iteration method (VIM) and matching it to a sequence of subintervals. Unlike the spectral method and the VIM, the proposed PSVIM does not require the solution of any linear or nonlinear system of equations and analytical integration.

Some well-known classes of Lane-Emden type equations are solved as examples to demonstrate the accuracy and easy implementation of this technique.

In this paper, a new and efficient technique is proposed to solve the nonlinear Lane-Emden equations. The proposed method overcomes the difficulties arising in calculating complicated and time-consuming integrals and terms that are not needed in the standard VIM.