Solving some ordinary differential equations numerically using differential evolution algorithm with a simple adaptive mutation scheme

Febrianti, Werry; Sidarto, Kuntjoro Adji; Sumarti, Novriana

doi:10.1063/5.0042351

Cited by 3 publications

(6 citation statements)

References 12 publications

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“…where w(x) and R(x) are denoting weight and residual functions respectively. In this paper, for simplicity purposes, the weight function can be assumed to be unit value, w(x) = 1 as in [4,10,11].…”

Section: Weighted Residual Methods As Optimization Problemmentioning

confidence: 99%

“…Based on Taylor explanation, the higher exponent can be approximated using sinus-cosines series with long enough series to get the highest accuracy such that using a Fourier series approximation like in reference [4,10,11]. But if this Fourier series approximation is used in solving stiff ordinary differential equations, then this Fourier series approximation is not effective to approximate the solution.…”

Section: A Series Of Trial Solution Of Odementioning

confidence: 99%

“…In this paper, we use the optimization method like in papers [4,8,10,11,18] for solving the stiff ordinary differential equation. We use a series expansion and weighted residual method for the approximation method in solving the stiff ordinary differential equation.…”

Section: Introductionmentioning

confidence: 99%

“…The series expansion and its derivative are implemented into ODEs and its boundary conditions. From here, we define a residual function with a unit weight function as in [4,10,11]. In our optimization problem, this function will be minimized using the Combinational Mutation Strategy of the Differential Evolution algorithm.…”

Section: Introductionmentioning

confidence: 99%

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An Approximate Optimization Method for Solving Stiff Ordinary Differential Equations With Combinational Mutation Strategy of Differential Evolution Algorithm

Febrianti

Sidarto

Sumarti

2022

mendel

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This paper examines the implementation of simple combination mutation of differential evolution algorithm for solving stiff ordinary differential equations. We use the weighted residual method with a series expansion to approximate the solutions of stiff ordinary differential equations. We solve the problems from an ordinary stiff differential equation for linear and nonlinear problems. Then, we also implement our method for solving stiff systems of ordinary differential equations. We find that our algorithm can approximate the exact solution of a stiff ordinary differential equation with the smallest error for each length of series that we have chosen. Thus, this approximation method, by using the optimization method of simple combination differential evolution, can be a good tool for solving stiff ordinary differential equations.

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Section: Weighted Residual Methods As Optimization Problemmentioning

confidence: 99%

Section: A Series Of Trial Solution Of Odementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Approximate Optimization Method for Solving Stiff Ordinary Differential Equations With Combinational Mutation Strategy of Differential Evolution Algorithm

Febrianti

Sidarto

Sumarti

2022

mendel

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“…First, we change the BS PDE into an optimization problem using a residual method. Before using this residual method to solve the BS PDE, we use this method to solve an ordinary differential equation (ODE) as presented in Febrianti et al [8] and Febrianti et al [9]. This method was inspired by Babaei [1] and Sadollah et al [22], who used a weighted residual method to solve ODEs.…”

Section: Introductionmentioning

confidence: 99%

Approximate Solution for Barrier Option Pricing Using Adaptive Differential Evolution With Learning Parameter

Febrianti

Sidarto

Sumarti

2022

mendel

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Black-Scholes (BS) equations, which are in the form of stochastic partial differential equations, are fundamental equations in mathematical finance, especially in option pricing. Even though there exists an analytical solution to the standard form, the equations are not straightforward to be solved numerically. The effective and efficient numerical method will be useful to solve advanced and non-standard forms of BS equations in the future. In this paper, we propose a method to solve BS equations using an approach of optimization problems, where a metaheuristic optimization algorithm is utilized to find the best-approximated solutions of the equations. Here we use the Adaptive Differential Evolution with Learning Parameter (ADELP) algorithm. The BS equations being solved are meant to find values of European option pricing that is equipped with Barrier option pricing. The result of our approximation method fits well to the analytical approximation solutions.

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Solving systems of ordinary differential equations using differential evolution algorithm with the best base vector of mutation scheme

Febrianti¹,

Sidarto²,

Sumarti³

2021

AIP Conference Proceedings

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Solving some ordinary differential equations numerically using differential evolution algorithm with a simple adaptive mutation scheme

Cited by 3 publications

References 12 publications

An Approximate Optimization Method for Solving Stiff Ordinary Differential Equations With Combinational Mutation Strategy of Differential Evolution Algorithm

An Approximate Optimization Method for Solving Stiff Ordinary Differential Equations With Combinational Mutation Strategy of Differential Evolution Algorithm

Approximate Solution for Barrier Option Pricing Using Adaptive Differential Evolution With Learning Parameter

Solving systems of ordinary differential equations using differential evolution algorithm with the best base vector of mutation scheme

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