Multi-derivative hybrid methods for integration of general second order differential equations

Kayode, John Stephen; Success, Abejide Kolawole

doi:10.26637/mjm0704/0042

Cited by 2 publications

(3 citation statements)

References 2 publications

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“…The method is promising since the computed results agreed with the exact solution up to at least (8) eight decimal places. Problem (2-5) was solved by Ogunware & Ezekiel [18], Kayode & Success [22] and Adeyefa [14] with h = 0.01. It was observed that the method performed better than Order Eight of Ogunware & Ezekiel [18], Order Six of Kayode & Success [22], and Order Seven of Adeyefa [14], shown in Tables 2-5.…”

Section: Discussionmentioning

confidence: 99%

“…Problem (2-5) was solved by Ogunware & Ezekiel [18], Kayode & Success [22] and Adeyefa [14] with h = 0.01. It was observed that the method performed better than Order Eight of Ogunware & Ezekiel [18], Order Six of Kayode & Success [22], and Order Seven of Adeyefa [14], shown in Tables 2-5. To further analyze the results of the test problems 1-5, the results in Table 1-5 are plotted in Figs.…”

Section: Discussionmentioning

confidence: 99%

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Advancing Numerical Methods of Block Multi-Derivative Approaches for ODEs of Various Orders

Olabode,

Kayode,

Olatubi

et al. 2024

Asian Res. J. Math.

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This work presents advancing numerical methods of block multi-derivative approaches for ordinary differential equations (ODEs) of Various Orders. The derivation of the methods is achieved by applying the techniques of interpolation and collocation to a power series polynomial, which is considered an approximate solution to the problems. Higher derivative terms are introduced to improve the accuracy of the method, giving room to modify the method for solving second and third-order initial value problems (IVPs) of ordinary differential equations (ODEs). Details conformation of the block method is presented, showing that the method is zero stable, consistent and convergent. The method is applied block-by-block to first, second and third-order initial value problems (IVPs) of ordinary differential equations. The application of the method to a real-life example also yields accurate results.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Advancing Numerical Methods of Block Multi-Derivative Approaches for ODEs of Various Orders

Olabode,

Kayode,

Olatubi

et al. 2024

Asian Res. J. Math.

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“…• Stochastic Differential Equation SDE Some Authors (example: Kayode S. J. and Abejide K. S. 2019) [12] had developed several numerical methods to solve some kind of differential equations, the methods established were found to be accurate using the test criterion widely studied from Lambert, J. D. 1991 [17] In this study SDEs as it related to fiancial mathematics were studied using knowledge from Operation Research [15] 1…”

Section: Types Of Differential Equationmentioning

confidence: 99%

Euler-Maruyama Approximation of Stochastic Dependent Poisson-Jump in Black-Scholes Asset Price Model

Kayode,

Abejide

2023

Theoretical Mathematics &Amp; Applications

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In this study, the Gaussian white noise and the differential Poisson of the Stochastic Differential Equation(SDE) with distributed jump are examined. Using Ito integral as a tool, a one step Euler-Maruyama (E-M) method is considered for the approximation of Stochastic Dependent Poisson Analysis (SDPA) in finance. The Deterministic Quadrature Rule (DQR) was used in the establishment of the method for easy examination of the Black-Scholes asset price model for stock investors; MATLAB package was used for simulation of the method. However the Mean Absolute Error (MAE) as well as Strong Order of Convergence (SOC) method was considered to ascertain its usability. The result clearly shows entry points and exit points of stock market. Consequently, the findings of this research is strongly recommended. Keywords: Euler-Maruyama method, Stochastic differential equation, Ito integral, Poisson distributed jump, Random variables, Deterministic model.

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Multi-derivative hybrid methods for integration of general second order differential equations

Cited by 2 publications

References 2 publications

Advancing Numerical Methods of Block Multi-Derivative Approaches for ODEs of Various Orders

Advancing Numerical Methods of Block Multi-Derivative Approaches for ODEs of Various Orders

Euler-Maruyama Approximation of Stochastic Dependent Poisson-Jump in Black-Scholes Asset Price Model

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