An efficient B-spline difference method for solving system of nonlinear parabolic PDEs

Aminikhah, Hossein; Alavi, Javad

doi:10.1007/s40324-017-0139-8

Cited by 7 publications

(11 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The maximum absolute errors at the final time

of the proposed method and some spline-based methods include; redefined cubic B-splines collocation (method I) [17] , [18] , cubic B-Spline Quasi-Interpolation (method II) [28] , [29] , [30] and B-spline differences (method III) [31] are reported in Table 1 . Furthermore, the error norms

and

for the proposed method and methods I, II and, III are tabulated in Table 2 .…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The maximum absolute errors at the final time

of the proposed method are compared with those of cubic B-Spline Quasi-Interpolation (Method II) [28] , [29] , B-spline differences (method III) [31] and a cubic B-splines collocation method (Method IV) [32] in Table 4 . Also, the error norms

and

corresponding to the suggested method and the methods II, III and, IV are expressed in Table 5 .…”

Section: Numerical Experimentsmentioning

confidence: 99%

See 1 more Smart Citation

Orthogonal cubic splines for the numerical solution of nonlinear parabolic partial differential equations

Alavi¹,

Aminikhah²

2023

MethodsX

Self Cite

View full text Add to dashboard Cite

“…The maximum absolute errors at the final time

and

for the proposed method and methods I, II and, III are tabulated in Table 2 .…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The maximum absolute errors at the final time

and

corresponding to the suggested method and the methods II, III and, IV are expressed in Table 5 .…”

Section: Numerical Experimentsmentioning

confidence: 99%

Orthogonal cubic splines for the numerical solution of nonlinear parabolic partial differential equations

Alavi¹,

Aminikhah²

2023

MethodsX

Self Cite

View full text Add to dashboard Cite

“…An approximation for a continuous function f is approximated by a linear combination of cubic B-Spline functions which could be defined as operators of the form [30,31].…”

Section: Cubic B-spline Quasi Interpolationmentioning

confidence: 99%

Biological treatment of slaughterhouse wastewater: kinetic modeling and prediction of effluent

Fard

Pendashteh

Alavi

2019

J Environ Health Sci Engineer

Self Cite

View full text Add to dashboard Cite

In this study three modeling approaches consisting Modified Stover-Kincannon, multilayer perceptron neural network (MLPANN) and B-Spline quasi interpolation were applied in order to predict effluent of up-flow anaerobic sludge blanket (UASB) reactor and also to find the reaction kinetics. At first run, the average total chemical oxygen demand (TCOD) removal efficiency was 48.3% with hydraulic retention time (HRT) of 26 h and 63.8% with HRT of 37 h, at OLR of 0.77-1.66 kg TCOD/m 3 d. At the second run, UASB reactor operated with OLR of 1.94-3.1 kg TCOD/m 3 d and achieved the average TCOD removal efficiency of 64.74 and 72.48% with HRT of 26 and 37 h, respectively. The Modified Stover-Kincannon performed well in terms of kinetic determination with a high value of regression coefficient over 0.98. The B-Spline quasi interpolation and MLPANN indicated a great fit for effluent prediction with average R of 0.9984 and 0.9986, and MSE of 157.6050 and 129.7796, respectively; however, they gave no information about reactions occurred in the system. Keywords Biological treatment. TCOD removal. Modified Stover-Kincannon. Artificial neural network. B-spline quasi interpolation Highlights • Performance of up-flow anaerobic sludge blanket reactor. • Effect of HRT on removal efficiency. • Multi-layer perceptron and B-Spline quasi interpolation were used in order to predict the effluent of UASB reactor. • Kinetic modeling of UASB reactor by modified Stover-Kincannon.

show abstract

“…On the other hand, implicit methods work with the whole system matrix, thus they can be extremely slow with huge memory usage when the number of cells is large. Still, these methods are typically used for solving these kinds of equations, see for example [10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…The values given in Equation ( 13) can be used to recalculate A new i again, which makes sense to repeat (13) to obtain new results. In this case, we have three stages altogether, thus the method is called the LNe3 method [38].…”

mentioning

confidence: 99%

A Comparative Study of Explicit and Stable Time Integration Schemes for Heat Conduction in an Insulated Wall

2022

View full text Add to dashboard Cite

Calculating heat transfer in building components is an important and nontrivial task. Thus, in this work, we extensively examined 13 numerical methods to solve the linear heat conduction equation in building walls. Eight of the used methods are recently invented explicit algorithms which are unconditionally stable. First, we performed verification tests in a 2D case by comparing them to analytical solutions, using equidistant and non-equidistant grids. Then we tested them on real-life applications in the case of one-layer (brick) and two-layer (brick and insulator) walls to determine how the errors depend on the real properties of the materials, the mesh type, and the time step size. We applied space-dependent boundary conditions on the brick side and time-dependent boundary conditions on the insulation side. The results show that the best algorithm is usually the original odd-even hopscotch method for uniform cases and the leapfrog-hopscotch algorithm for non-uniform cases.

show abstract

An efficient B-spline difference method for solving system of nonlinear parabolic PDEs

Cited by 7 publications

References 14 publications

Orthogonal cubic splines for the numerical solution of nonlinear parabolic partial differential equations

Orthogonal cubic splines for the numerical solution of nonlinear parabolic partial differential equations

Biological treatment of slaughterhouse wastewater: kinetic modeling and prediction of effluent

A Comparative Study of Explicit and Stable Time Integration Schemes for Heat Conduction in an Insulated Wall

Contact Info

Product

Resources

About