Numerical integration of partial differential equations using cubic splines

Wang, Pu; Kahawita, R.

doi:10.1080/00207168308803369

Cited by 114 publications

(44 citation statements)

References 2 publications

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“…Therefore numerical studies of the equation are of interest in explaining physical phenomena such as shallow water waves and ion acoustic plasma waves. The cubic spline collocation procedure and its application have been widely used in the numerical solution of partial differential equations (PDEs) [5,[14][15][16] because they possess some advantages over other numerical methods without the disadvantages of being computationally intensive and having a complex problem formulation. Various numerical schemes for obtaining the numerical solution of the RLW equation incorporating spline functions have been set up.…”

Section: U X (At) = 0 U X (Bt) = 0 ---And Initial Conditionsmentioning

confidence: 99%

Numerical integration of the RLW equation using cubic splines

2005

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Section: U X (At) = 0 U X (Bt) = 0 ---And Initial Conditionsmentioning

confidence: 99%

Numerical integration of the RLW equation using cubic splines

2005

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“…12-13, and the appropriate boundary conditions, Eqs. 15-16, can be solved by the cubic spline collocation method for θ and φ (Wang and Kahawita 1983). Moreover, the Simpson's rule for variable grids is used to calculate the value of f at every position from the values of f calculated from Eq.…”

Section: Discussionmentioning

confidence: 99%

“…This problem has not been studied. A coordinate transformation is used to derive nondimensional boundary-layer governing equations, and the obtained nonsimilar equations are then solved by the cubic spline collocation method (Wang and Kahawita 1983). The effects of the Soret parameter, the Dufour parameter, the Lewis number, the buoyancy ratio, and the power-law exponent on the local surface temperature and the local surface concentration over a vertical truncated cone in a fluid-saturated porous medium with variable wall heat and mass fluxes are carefully examined.…”

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confidence: 99%

Soret and Dufour Effects on Double-Diffusive Free Convection Over a Vertical Truncated Cone in Porous Media with Variable Wall Heat and Mass Fluxes

Cheng

2011

Transp Porous Med

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This work studies the Soret and Dufour effects on the double-diffusive free convection over a downward-pointing vertical truncated cone with variable wall heat and mass fluxes in fluid-saturated porous media. A coordinate transformation is used to derive the nondimensional boundary-layer governing equations, and the obtained nonsimilar equations are then solved by the cubic spline collocation method. Results for local surface temperature and the local surface concentration are presented as functions of Soret parameters, Dufour parameters, power-law exponents, buoyancy ratios, and Lewis numbers. Results show that increasing the Dufour parameter tends to increase the local surface temperature, while it tends to decrease the local surface concentration. An increase in the Soret number leads to a decrease in the local surface temperature for buoyancy assisting flows, while it leads to an increase in the local surface temperature for buoyancy opposing flows. Increasing the Soret number tends to increase the local surface concentration. Moreover, the local surface temperature and the local surface concentration of the truncated cones with higher power-law exponents are lower than those with lower exponents.

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“…An improved version of the cubic spline collocation method [40] is used to perform numerical computation in this study [41]. Using cubic spline collocation, Equations (14a)-(14d) can be written as: …”

Section: Methodsmentioning

confidence: 99%

The Effect of Thermal Radiation on Entropy Generation Due to Micro-Polar Fluid Flow Along a Wavy Surface

Chen

Yang

Chang

2011

Entropy

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Abstract:In this study, the effect of thermal radiation on micro-polar fluid flow over a wavy surface is studied. The optically thick limit approximation for the radiation flux is assumed. Prandtl's transposition theorem is used to stretch the ordinary coordinate system in certain directions. The wavy surface can be transferred into a calculable plane coordinate system. The governing equations of micro-polar fluid along a wavy surface are derived from the complete Navier-Stokes equations. A simple transformation is proposed to transform the governing equations into boundary layer equations so they can be solved numerically by the cubic spline collocation method. A modified form for the entropy generation equation is derived. Effects of thermal radiation on the temperature and the vortex viscosity parameter and the effects of the wavy surface on the velocity are all included in the modified entropy generation equation.

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Numerical integration of partial differential equations using cubic splines

Cited by 114 publications

References 2 publications

Numerical integration of the RLW equation using cubic splines

Numerical integration of the RLW equation using cubic splines

Soret and Dufour Effects on Double-Diffusive Free Convection Over a Vertical Truncated Cone in Porous Media with Variable Wall Heat and Mass Fluxes

The Effect of Thermal Radiation on Entropy Generation Due to Micro-Polar Fluid Flow Along a Wavy Surface

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