Numerical verification of the orders of accuracy of truncated asymptotic expansion solutions to the van der Pol equation

Mungkasi, Sudi

doi:10.1007/s10910-020-01191-6

Cited by 7 publications

(4 citation statements)

References 11 publications

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“…With the success of our strategies involved in the proposed model and method, we believe that these results could be extended further in other fluid mechanics and heat transfer areas as well as initial-boundary value problems. One could implement our strategies to various problems (to mention some of them, see Alawi and Kamar [19], Bindu et al, [20], Ewis [21], Ferdows et al, [22], Ghani and Jami [23], Giap and Kosuke [24], Jamil et al, [25], Mohamed et al, [26], Sahak et al, [27] and the work of Mungkasi [28,29] as well as Mungkasi and Roberts [30]). Each of these problems could be explored and solved in their own rights.…”

Section: Results and Discussion For The Proposed Modelmentioning

confidence: 99%

Modelling And Simulation of Topical Drug Diffusion in The Dermal Layer of Human Body

Mungkasi

2021

ARFMTS

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We consider the problem of drug diffusion in the dermal layer of human body. Two existing mathematical models of the drug diffusion problem are recalled. We obtain that the existing models lead to inconsistent equations for the steady state condition. We also obtain that solutions to the existing models are unrealistic for some cases of the unsteady state condition, because negative drug concentrations occur due to the inappropriate assumption of the model. Therefore, in this paper, we propose a modified mathematical model, so that the model is consistent, and the solution is nonnegative for both steady and unsteady state conditions of the drug diffusion problem in the dermal layer of human body. For the steady state condition, the exact solution to the proposed model is given. For unsteady state condition, we use a finite difference method for solving the models numerically, where the discretisation is centred in space and forward in time. Simulation results confirm that our proposed model and method preserve the non-negativity of the solution to the problem, so the solution is more realistic than that of the old model.

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Section: Results and Discussion For The Proposed Modelmentioning

confidence: 99%

Modelling And Simulation of Topical Drug Diffusion in The Dermal Layer of Human Body

Mungkasi

2021

ARFMTS

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“…The network was trained with thirty equidistant points at interval [0, 2] for computing the results. Comparison between fourth-fifth order Runge-Kutta (RK45), Homotopy Analysis Method (HAM) and Chebyshev neural results (ChNN) are showed in Table (10) when F(z)=sinh(z), M=5;7, α = 0.5, β = −0.5, µ = 0.1, ω = 0.79 and f = 0.5. Values of weights for ChNN method when F(z)=sinh(z), M=5; 7, α = 0.5, β = −0.5, µ = 0.1, ω = 0.79 and f = 0.5 have been shown in Table (11).…”

Section: Duffing-van Der Pol Oscillatorsmentioning

confidence: 99%

“…Motsa and Sibanda presented a novel application of the successive linearisation method to the Van der Pol duffing oscillator equations [7]. A differential transformation method has been implemented to study the Van der Pol duffing oscillator equation [8,9,10,11]. Soomro et al investigated and compared among improved Heun's method, Runge-Kutta order fourth and mid-point method to show that the Runge-Kutta method can obtain better accuracy compare to the Heun and mid-point method [12].…”

Section: Introductionmentioning

confidence: 99%

Application of Chebyshev neural network to solve Van der Pol equations

Chaharborj

See²

2021

IJBAS

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In dynamics, the Van der Pol oscillator is a non-conservative oscillator with non-linear damping. The problems of single-well, double-well and double-hump Van der Pol-Dufing equations are studied in this paper. The Chebyshev Neural Network (ChNN) model will be applied to obtain the numerical solutions of these types of equations for the first time. The hidden layer is eliminated by expanding the input pattern by Chebyshev polynomials which employs a single layer neural network. In order to modify the network parameters and to minimize the computed error function, a feed forward neural network model with error back propagation principle is used. The obtained numerical results form the ChNN model will be compared with the analytical solutions, namely Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM), Differential Transform Method (DTM) and exact. Comparisons of the solutions obtained with existing numerical results show that this method is a capable tool for solving this kind of nonlinear problems.

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“…The unsaturated and saturated steady state solutions to the initial value problem have been obtained by Rahamathunissa and Rajendran [10] using a variational iteration method. The variational iteration method was due to He [12,13,14] and it has been successfully used to solve various problems [15,16,17,18,19,20,21,22,23,24] including the mathematical chemistry areas [25,26,27,28,29,30].…”

Section: Introductionmentioning

confidence: 99%

Some Numerical and Analytical Solutions to an Enzyme-Substrate Reaction-Diffusion Problem

Mungkasi

2020

2020 3rd International Seminar on Research of Information Technology and Intelligent Systems (ISRITI)

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Numerical verification of the orders of accuracy of truncated asymptotic expansion solutions to the van der Pol equation

Cited by 7 publications

References 11 publications

Modelling And Simulation of Topical Drug Diffusion in The Dermal Layer of Human Body

Modelling And Simulation of Topical Drug Diffusion in The Dermal Layer of Human Body

Application of Chebyshev neural network to solve Van der Pol equations

Some Numerical and Analytical Solutions to an Enzyme-Substrate Reaction-Diffusion Problem

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