Kamal Raslan

Author Statistics

Papers

Citation

H-Index

i-10 index

Research Field

Numerical Study for Heat Transfer in Symmetric Porous Channel with Expanding or Contracting Walls and Slip Boundary Condition

Kamal Raslan Zain F. Abu Shaeer

The homotopy analysis method (HAM) is implemented t o obtain the approximate solutions of the nonlinear evolution equations in m athematical physics. The results obtained by this method have a good agreeme nt with one obtained. It illustrates the validity and the great potential of the homotopy analysis method in solving partial differential equations.

Homotopy Analysis Method

Homotopy perturbation method

Source

Cite

Citations (1)

KKL-model of MHD CuO-nanofluid flow over a stagnation point stretching sheet with nonlinear thermal radiation and suction/injection

Results in Physics (2018)

S. A. Mohammadein Kamal Raslan Mohamed Abdelwahed Elsayed M. Abedel-aal

In this study, we analyzed numerically the effects of magnetic field and thermal radiation on forced-convection flow of CuO-water nanofluid past a stretching sheet with stagnation point in the presence of suction/injection. Considering the effects of Brownian motion, we applied the Koo–Kleinstreuer–Li (KKL) correlation to simulate the effective thermal conductivity and viscosity of the nanofluid. The equations governing the flow transformed to ordinary differential equations and solved numerically using the fourth-order Runge–Kutta integration scheme featuring a shooting technique. The influence of significant parameters such as the magnetic parameter, radiation parameter, suction/injection parameter and velocity ratio parameter on the velocity and temperature profiles are discussed and presented through graphs and analyzed for (CuO-water).

Thermal Radiation

Shooting method

Stagnation temperature

10.1016/j.rinp.2018.05.032

Cite

Citations (66)

Solving systems of ordinary differential equations in unbounded domains by exponential Chebyshev collocation method

DOAJ (DOAJ: Directory of Open Access Journals) (2016)

Mohamed Ramadan Kamal Raslan Talaat El Danaf Mohamed A. Abd Elsalam Mohamed Ramadan

Collocation (remote sensing)

Source

Cite

Citations (4)

Adomian decomposition method for Burger's–Huxley and Burger's–Fisher equations

Applied Mathematics and Computation (2004)

Hassan N.A. Ismail Kamal Raslan Aziza A. Abd Rabboh

Adomian decomposition method

10.1016/j.amc.2003.10.050

Cite

Citations (191)

A new exponential Chebyshev operational matrix of derivatives for solving high-order ordinary differential equations in unbounded domains

Journal of Modern Methods in Numerical Mathematics (2016)

Mohamed Ramadan Kamal Raslan Talaat El Danaf Mohamed A. Abd Elsalam

The purpose of this paper is to investigate a new exponential Chebyshev (EC) operational matrix of derivatives. The new operational matrix of derivatives of the EC functions is derived and introduced for solving high-order linear ordinary differential equations with variable coefficients in unbounded domain using the collocation method. This method transforms the given differential equation and conditions to matrix equation with unknown EC coefficients. These matrices together with the collocation method are utilized to reduce the solution of high-order ordinary differential equations to the solution of a system of algebraic equations. The solution is obtained in terms of EC functions. Numerical examples are given to demonstrate the validity and applicability of the method. The obtained numerical results are compared with others existing methods and the exact solution where it shown to be very attractive with good accuracy.

Matrix Exponential

Orthogonal collocation

Matrix (chemical analysis)

Exponential integrator

Algebraic equation

10.20454/jmmnm.2016.1068

Cite

Citations (6)

Solving systems of high-order linear ordinary differential equations with variable coefficients by means of exponential Chebyshev collocation method

Journal of Modern Methods in Numerical Mathematics (2017)

Mohamed Ramadan Kamal Raslan Talaat El Danaf Mohamed A. Abd Elsalam

The purpose of this paper is to investigate the use of exponential Chebyshev (EC) collocation method for solving systems of high-order linear ordinary differential equations with variable coefficients with new scheme, using the EC collocation method in unbounded domains. The EC functions approach deals directly with infinite boundaries without singularities. The method transforms the system of differential equations and the given conditions to block matrix equations with unknown EC coefficients. By means of the obtained matrix equations, a new system of equations which corresponds to the system of linear algebraic equations is gained. Numerical examples are given to illustrative the validity and applicability of the method.

Coefficient matrix

Orthogonal collocation

Matrix Exponential

Chebyshev iteration

Exponential integrator

Algebraic equation

Reduction of order

Independent equation

Collocation (remote sensing)

10.20454/jmmnm.2017.1131

Cite

Citations (3)

Finite difference method with different high order approximations for solving complex equation

New Trends in Mathematical Science (2017)

Kamal Raslan Talaat S. El‐Danaf Khalid K. Ali

In this paper, we take finite difference method with different high order approximations for solving Hirota Equation is presented.The stability analysis using Von-Neumann technique shows schemes are unconditionally stable.To test accuracy the error norms L 2 , L ∞ are computed.We compute local truncation error for different schemes.We make comparison between these approximations through the results that we are get it.These results show that the approximation of O(k 2 + h 4 ) introduced here is more accurate than others and easy to apply.

Finite difference

Approximations of π

10.20852/ntmsci.2017.119

Cite

Citations (7)

Numerical solution of high-order linear integro differential equations with variable coefficients using two proposed schemes for rational Chebyshev functions

New Trends in Mathematical Science (2016)

Mohamed Ramadan Kamal Raslan Adel R. Hadhoud Mahmoud Nassar

In this paper, a rational Chebyshev (RC) collocation method is presented to solve high-order linear Fredholm integrodifferential equations with variable coefficients under the mixed conditions, in terms of RC functions by two proposed schemes.The proposed method converts the integral equation and its conditions to matrix equations, by means of collocation points on the semiinfinite interval, which corresponding to systems of linear algebraic equations in RC coefficients unknowns.Thus, by solving the matrix equation, RC coefficients are obtained and hence the approximate solution is expressed in terms of RC functions.Numerical examples are given to illustrate the validity and applicability of the method.The proposed method numerically compared with others existing methods as well as the exact solutions where it maintains better accuracy.

Algebraic equation

Chebyshev iteration

Coefficient matrix

Matrix (chemical analysis)

Collocation (remote sensing)

Chebyshev nodes

10.20852/ntmsci.2016318802

Cite

Citations (11)

The Tanh Methods for the Hirota Equations

International Journal of Computer Applications (2014)

Kamal Raslan Zain F. Abu Shaeer

In this paper we applied the tanh method for analytic study of the nonlinear equations of partial differential equations(PDEs).The proposed method gives more general exact traveling wave solutions without much extra effort.Three applications from literature of nonlinear equation of PDEs were solved by the method.The calculations demonstrate the effectiveness and convenience of the method for nonlinear sub system of PDEs.

10.5120/18793-0134

Cite

Citations (3)

A NEW IMPROVED SCHEME FOR PARTIAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS IN SEMI-INFINITE DOMAIN VIA DOUBLE RATIONAL CHEBYSHEV FUNCTIONS

Al-Azhar Bulletin of Science (2020)

Mahmoud Nassar Kamal Raslan Mohamed A. Ramadan

The concept of double rational Chebyshev functions on the semi-infinite domain () and some of their properties are introduced in this work.Also, the definition of derivatives for double rational Chebyshev functions is improved.This new definition is employed to deal with partial differential equations with variable coefficients derived on the interval [0, ) .The new definition with the spectral collocation method generates a new improved scheme.Numerical results are show that demonstrates the validity and applicability of the two techniques.The obtained numerical results are compared with the exact solution where it shown to be very attractive with good accuracy.

Chebyshev pseudospectral method

Chebyshev iteration

Chebyshev nodes

10.21608/absb.2020.111484

Cite

Citations (0)