In this work, we use the explicit and the implicit finite-difference methods to solve the nonlocal problem that consists of the diffusion equations together with nonlocal conditions. The nonlocal conditions for these partial differential equations are approximated by using the composite trapezoidal rule, the composite Simpson's 1/3 and 3/8 rules. Also, some numerical examples are presented to show the efficiency of these methods.

  In this paper, we use the repeated corrected Simpson's 3/8 quadrature method for obtaining the numerical solutions of Fredholm linear integral equations of the second kind. This method is more accurately than the repeated corrected Trapezoidal method and the repeated Simpson's 3/8 method. To illustrate the accuracy of this method, we give a numerical example

Intrinsic viscosities have been studied for polyethylene oxide in water which has wide industrial applications. The polyethylene oxide samples had two different structures, the first one was linear and covers a wide range of molecular weight of 1, 3, 10, 20, 35, 99, 370, 1100, 4600, and 8000 kg/mol and the second one was branched and had molecular weights of 0.55 and 40 kg/mol.
Intrinsic viscosities and Huggins constants have been determined for all types and molecular weights mentioned above at 25ºC using a capillary viscometer. The values of Mark-Houwink parameters (K and a) were equal to 0.0068 ml/g and 0.67 respectively, and have not been published for this range of molecular weight in as yet.

     In this paper, the Adomian decomposition method (ADM) is successfully applied to find the approximate solutions for the system of fuzzy Fredholm integral equations (SFFIEs) and we also study the convergence of the technique. A consistent way to reduce the size of the computation is given to reach the exact solution. One of the best methods adopted to determine the behavior of the approximate solutions. Finally, the problems that have been addressed confirm the validity of the method  applied in this research using a comparison by combining numerical methods such as the Trapezoidal rule and Simpson rule with ADM.

In this paper, author’s study sub diffusion bio heat transfer model and developed explicit finite difference scheme for time fractional sub diffusion bio heat transfer equation by using caputo fabrizio fractional derivative. Also discussed conditional stability and convergence of developed scheme. Furthermore numerical solution of time fractional sub diffusion bio heat transfer equation is obtained and it is represented graphically by Python.

The integral transformations is a complicated function from a function space into a simple function in transformed space. Where the function being characterized easily and manipulated through integration in transformed function space. The two parametric form of SEE transformation and its basic characteristics have been demonstrated in this study. The transformed function of a few fundamental functions along with its time derivative rule is shown. It has been demonstrated how two parametric SEE transformations can be used to solve linear differential equations. This research provides a solution to population growth rate equation. One can contrast these outcomes with different Laplace type transformations

   The Compressional-wave (Vp) data are useful for reservoir exploration, drilling operations, stimulation, hydraulic fracturing employment, and development plans for a specific reservoir. Due to the different nature and behavior of the influencing parameters, more complex nonlinearity exists for Vp modeling purposes. In this study, a statistical relationship between compressional wave velocity and petrophysical parameters was developed from wireline log data for Jeribe formation in Fauqi oil field south Est Iraq, which is studied using single and multiple linear regressions. The model concentrated on predicting compressional wave velocity from petrophysical parameters and any pair of shear waves velocity, porosity, density, a

       In this work, we prove that the triple linear partial differential equations (PDEs) of elliptic type (TLEPDEs) with a given classical continuous boundary control vector (CCBCVr) has a unique "state" solution vector (SSV)  by utilizing the Galerkin's method (GME). Also, we prove the existence of a classical continuous boundary optimal control vector (CCBOCVr) ruled by the TLEPDEs. We study the existence solution for the triple adjoint equations (TAJEs) related with the triple state equations (TSEs). The Fréchet derivative (FDe) for the objective function is derived. At the end we prove the necessary "conditions" theorem (NCTh) for optimality for the problem.