Cool roof is gaining popularity as a passive building energy saving solution. A concise and
easy-to-apply mathematical model is essential for building designers to evaluate the impact …

Double-skin roof is a popular passive cooling solution to curb heat gain into buildings and
cool roof is another emerging solution. This study proposed a novel CRHT (cool roof heat …

We investigate the approximate solution to a class of fourth-order Volterra–Fredholm integro
differential equations (VFIDEs). Additionally, we are able to get some adequate results for …

In this paper, two collocation methods based on the shifted Legendre polynomials are
proposed for solving system of nonlinear Fredholm-Volterra integro-differential equations …

In this paper, an algorithm is proposed to find an approximate solution for the Kirchhoff-type
nonlinear differential equation, which describes the static state of a beam. The solution of the …

Partial differential equations (PDEs) arise naturally in a wide variety of scientific areas and
applications, and their numerical solutions are highly indispensable in many cases. Typical …

In this paper, we consider a boundary value problem (BVP) for a fourth-order nonlinear
integro-differential equation. By reducing the problem to an operator equation, we establish …

In the tropics, the earth surface receives abundant solar radiation annually contributing
significantly to building heat gain and, thus, cooling demand. An effective method that can …

This paper is concerned with the existence and uniqueness of positive solution for the fourth
order Kirchhoff type problem $$\left\{\begin {array}{ll} u''''(x)-(a+ b\int_0^ 1 (u'(x))^ 2dx) …

abstract We investigate the approximate solution to a class of fourth-order Volterra–
Fredholm integro differential equations (VFIDEs). Additionally, we are able to get some …