Numerical investigation of the MHD suction–injection model of viscous fluid using a kernel-based method

Effects of heat transfer on MHD suction–injection model of viscous fluid flow through differential transformation and Bernoulli wavelet techniques

“…On the basis of the numerical methods of Section 4, the wavelet‐numerical and differential transform methods are developed to study the problem of various flow parameters on the distributions of velocity and temperature for both the suction and injection situations. Table 1 lists the approximate values of $$f^{\prime} (\eta )$$ for ( S , M , A ) = (0.1, 0.2, 0.1) and ( S , M , A ) = (0.4, 2, 1) are compared with those published 63 . For ( M , S ) = (0.2, 0.1) and various values of A , the approximation of $$f^{\prime\prime} (1)$$ is presented in Table 2.…”

“…The upper disk at $$z=h(t)$$ is moving with velocity $$\frac{-\alpha H}{2\sqrt{1-\alpha t}}$$ towards the stationary lower disk at $$z=0$$. Under the usual assumption in the literature, continuity, momentum, and energy equations are considered 63 $$$\nabla \cdot \overrightarrow{q}=0,$$$ $$$\rho \left(\frac{\partial \overrightarrow{q}}{\partial t}+(\overrightarrow{q}\cdot \nabla )\overrightarrow{q}\right)=-\nabla p+\mu {\nabla }^{2}\overrightarrow{q}+\sigma (\overrightarrow{q}\times B)\times B,$$$ $$$\frac{\partial T}{\partial t}+(\overrightarrow{q}\cdot \nabla )T=\frac{{k}_{f}}{{(\rho {c}_{p})}_{f}}{\nabla }^{2}T+\frac{{D}_{T}}{{T}_{m}}(\nabla \overrightarrow{q}\cdot \nabla \overrightarrow{q}).$$$…”

A kernel‐based method for solving the time‐fractional diffusion equation

“…He called these functions as “positive definite kernels.” The concept of reproducing kernels was systematized by Aronszajn [18] around 1948. From 1980, Cui and co‐workers [19, 20] are pioneers in linear and nonlinear numerical analysis based on “reproducing kernel theory.” Recently, a lot of research works have been devoted to the application of reproducing kernel Hilbert space method to solve several linear and nonlinear problems such as variational problems depending on indefinite integrals [21], delay differential equations of fractional order [22], nonlocal initial‐boundary value problems for hyperbolic and parabolic integro‐differential equations [23], Black–Scholes equation [24] and so on [25–27].…”

A pseudo-spectral method based on reproducing kernel for solving the time-fractional diffusion-wave equation

“…From 1980, Cui and co-workers [33,34] have been pioneers and beginners in the numerical analysis of linear and nonlinear problems using the "reproducing kernel Hilbert space method". Recently, a lot of research has been done to solve several linear and nonlinear problems using the theory of reproducing kernel [35][36][37][38][39][40][41][42][43][44][45][46].…”