scholarly journals Analysis of compartments-in-series models of liver metabolism as partial differential equations: the effect of dispersion and number of compartments

2019 ◽  
Vol 16 (3) ◽  
pp. 1082-1114 ◽  
Author(s):  
Marcella Noorman ◽  
◽  
Richard Allen ◽  
Cynthia J. Musante ◽  
H. Thomas Banks ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Liver Metabolism ◽  
Partial Differential ◽  
In Series

scholarly journals Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 335 ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Muhammad Arif ◽  
Poom Kumam
Keyword(s):  
Partial Differential Equations ◽  
Analytical Solution ◽  
Differential Equations ◽  
Fractional Order ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Third Order ◽  
Partial Differential ◽  
Adomian Decomposition ◽  
In Series

In the present article, we related the analytical solution of the fractional-order dispersive partial differential equations, using the Laplace–Adomian decomposition method. The Caputo operator is used to define the derivative of fractional-order. Laplace–Adomian decomposition method solutions for both fractional and integer orders are obtained in series form, showing higher convergence of the proposed method. Illustrative examples are considered to confirm the validity of the present method. The fractional order solutions that are convergent to integer order solutions are also investigated.

scholarly journals Effective Method for Solving Different Types of Nonlinear Fractional Burgers’ Equations

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 729 ◽  
Author(s):  
Safyan Mukhtar ◽  
Salah Abuasad ◽  
Ishak Hashim ◽  
Samsul Ariffin Abdul Karim
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Approximate Solutions ◽  
Three Dimensions ◽  
Partial Differential ◽  
Transform Method ◽  
Burgers Equations ◽  
Different Types ◽  
In Series

In this study, a relatively new method to solve partial differential equations (PDEs) called the fractional reduced differential transform method (FRDTM) is used. The implementation of the method is based on an iterative scheme in series form. We test the proposed method to solve nonlinear fractional Burgers equations in one, two coupled, and three dimensions. To show the efficiency and accuracy of this method, we compare the results with the exact solutions, as well as some established methods. Approximate solutions for different values of fractional derivatives together with exact solutions and absolute errors are represented graphically in two and three dimensions. From all numerical results, we can conclude the efficiency of the proposed method for solving different types of nonlinear fractional partial differential equations over existing methods.

scholarly journals A Collocation Method Using Radial Polynomials for Solving Partial Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1419 ◽  
Author(s):  
Cheng-Yu Ku ◽  
Jing-En Xiao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Collocation Method ◽  
Shape Parameter ◽  
Taylor Series Expansion ◽  
Three Dimensions ◽  
Partial Differential ◽  
In Series ◽  
Even Order ◽  
Kansa Method

In this article, a collocation method using radial polynomials (RPs) based on the multiquadric (MQ) radial basis function (RBF) for solving partial differential equations (PDEs) is proposed. The new global RPs include only even order radial terms formulated from the binomial series using the Taylor series expansion of the MQ RBF. Similar to the MQ RBF, the RPs is infinitely smooth and differentiable. The proposed RPs may be regarded as the equivalent expression of the MQ RBF in series form in which no any extra shape parameter is required. Accordingly, the challenging task for finding the optimal shape parameter in the Kansa method is avoided. Several numerical implementations, including problems in two and three dimensions, are conducted to demonstrate the accuracy and robustness of the proposed method. The results depict that the method may find solutions with high accuracy, while the radial polynomial terms is greater than 6. Finally, our method may obtain more accurate results than the Kansa method.

scholarly journals Natural Transform Decomposition Method for Solving Fractional-Order Partial Differential Equations with Proportional Delay

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 532 ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Poom Kumam ◽  
Muhammad Arif ◽  
Dumitru Baleanu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Present Article ◽  
Fractional Order ◽  
Present Method ◽  
Decomposition Method ◽  
Proportional Delay ◽  
Partial Differential ◽  
Analytical Technique ◽  
In Series

In the present article, fractional-order partial differential equations with proportional delay, including generalized Burger equations with proportional delay are solved by using Natural transform decomposition method. Natural transform decomposition method solutions for both fractional and integer orders are obtained in series form, showing higher convergence of the proposed method. Illustrative examples are considered to confirm the validity of the present method. Therefore, Natural transform decomposition method is considered to be one of the best analytical technique, to solve fractional-order linear and non-linear Partial deferential equations particularly fractional-order partial differential equations with proportional delay.

scholarly journals Analytical Analysis of Fractional-Order Multi-Dimensional Dispersive Partial Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 939
Author(s):  
Shuang-Shuang Zhou ◽  
Mounirah Areshi ◽  
Praveen Agarwal ◽  
Nehad Ali Shah ◽  
Jae Dong Chung ◽  
...  
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Decomposition Method ◽  
Approximate Solutions ◽  
Partial Differential ◽  
Suggested Technique ◽  
In Series ◽  
Fractional Orders

In this paper, a novel technique called the Elzaki decomposition method has been using to solve fractional-order multi-dimensional dispersive partial differential equations. Elzaki decomposition method results for both integer and fractional orders are achieved in series form, providing a higher convergence rate to the suggested technique. Illustrative problems are defined to confirm the validity of the current technique. It is also researched that the conclusions of the fractional-order are convergent to an integer-order result. Moreover, the proposed method results are compared with the exact solution of the problems, which has confirmed that approximate solutions are convergent to the exact solution of each problem as the terms of the series increase. The accuracy of the method is examined with the help of some examples. It is shown that the proposed method is found to be reliable, efficient and easy to use for various related problems of applied science.

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