The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimi

In this paper, we consider a new approach to solve type of partial differential equation by using coupled Laplace transformation with decomposition method to find the exact solution for non–linear non–homogenous equation with initial conditions. The reliability for suggested approach illustrated by solving model equations such as second order linear and nonlinear Klein–Gordon equation. The application results show the efficiency and ability for suggested approach.

Background: The objectives of this study are to evaluate the effect of addition of Multi-Wall Carbon Nano Tubes (MWCNTs) of different concentrations (0.05 mg.mL-1,0.25 mg.mL-1,0.5 mg.mL-1and1 mg.mL-1) on dimethyl sulphoxide DMSO and distilled water (DW) on tooth enamel. It intends to evaluate enamel microhardness in (Kg. m-2) pre and post the application of Multi-Wall Carbon Nano Tubes (MWCNTs). Materials and Methods: Thirty specimens prepared for the present study to measure the hardness of the enamel. Results: The results showed that a significant increase in the enamel microhardness for groups 0.05 mg/mL (group B), 0.25 mg/mL (group C), 0.5 mg/mL (group D) and 1 mg/mL (group E) compared with control group (group A) in dimethyl sulphoxi

Two-dimensional unsteady mixed convection in a porous cavity with heated bottom wall is numerically studied in the present paper. The forced flow conditions are imposed by providing a hydrostatic pressure head at the inlet port that is located at the bottom of one of the vertical side walls and an open vent at the top of the other vertical side wall. The Darcy model is adopted to model the fluid flow in the porous medium and the combination effects of hydrostatic pressure head and the heat flux quantity parameters are carefully investigated. These governing parameters are varied over wide ranges and their effect on the heat transfer characteristics is studied in detail. It is found that the time required to reach a desired temperature at th

Porous asphalt paving is a modern design method that differs from the usual asphalt pavements' traditional designs. The difference is that the design structure of porous pavements allows the free passage of fluids through their layers, which controls or reduces the amount of runoff or water accumulated in the area by allowing the flow of rain and surface runoff.  The cross-structure of this type of paving works as a suitable method for managing rainwater and representing groundwater recharge. The overall benefits of porous asphalt pavements include environmental services and safety features, including controlling the build-up of contaminated metals on the road surface, rainwater management, resistance to slipping ac