Page 653 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 653
NUMERICAL ANALYSIS AND SCIENTIFIC COMPUTING
with fundamental matrix of system. Using these representations we compile a system of linear
algebraic equations with respect to parameters. We proposed algorithm for finding of numer-
ical solution to the equivalent problem [2]. This algorithm includes the numerical solving of
the Cauchy problems for system of the ordinary differential equations and solving of the linear
system of algebraic equations.
References
[1] Dzhumabaev D. S. Criteria for the unique solvability of a linear boundary-value problem
for an ordinary differential equation. Comput. Maths. Math. Phys 29 (1) (1989), 34-46.
[2] Assanova A. T., Imanchiev A. E., Kadirbayeva Zh. M. Numerical solution of systems of
loaded ordinary differential equations with multipoint conditions. Computational mathe-
matics and mathematical physics 58 (4) (2018), 508-516.
A stochastic numerical scheme for SDEs with fBm under non-Lipschitz
coefficient
Minoo Kamrani, m.kamrani@razi.ac.ir
Razi university, Islamic Republic of Iran
Our aim is to propose a numerical method for the solution of stochastic differential equa-
tions(SDEs) with fractional Brownian motion(fBM) which the diffusion coefficient is non-
Lipschitz. We consider fractional Brownian motions with Hurst parameter 1 < H < 1.
2
The basic idea is to apply Lamperti transformation to obtain a stochastic differential equa-
tion with additive noise. The well-posedness of this equation is proved and by applying a
numerical method which is based on Euler scheme, the solution of the transformed equation is
derived. Therefore, by using the inverse of the Lamperti transformation, numerical solution of
the main SDE is established.
Based on the properties of the Malliavin calculus, convergence of the proposed method is
explained. Furthermore the strong rate of convergence is derived.
A numerical solution to a nonlinear boundary value problem for the
Fredholm integro-differential equation
Sandugash Mynbayeva, mynbaevast80@gmail.com
Institute of mathematics and mathematical modeling, Kazakhstan
It is considered the boundary value problem (BVP) for the Fredholm IDE
dx m T t ∈ (0, T ), x ∈ Rn,
= f (t, x) + ϕk(t) ψk(τ )x(τ )dτ, (1)
dt
k=1 0
g [x(0), x(T )] = 0, (2)
where f : [0, T ] × Rn → Rn and g : Rn × Rn → Rn are continuous; the n × n matrices ϕk(t),
ψk(τ ), k = 1, m, are continuous on [0, T ], x = max |xi|.
i=1,n
651
with fundamental matrix of system. Using these representations we compile a system of linear
algebraic equations with respect to parameters. We proposed algorithm for finding of numer-
ical solution to the equivalent problem [2]. This algorithm includes the numerical solving of
the Cauchy problems for system of the ordinary differential equations and solving of the linear
system of algebraic equations.
References
[1] Dzhumabaev D. S. Criteria for the unique solvability of a linear boundary-value problem
for an ordinary differential equation. Comput. Maths. Math. Phys 29 (1) (1989), 34-46.
[2] Assanova A. T., Imanchiev A. E., Kadirbayeva Zh. M. Numerical solution of systems of
loaded ordinary differential equations with multipoint conditions. Computational mathe-
matics and mathematical physics 58 (4) (2018), 508-516.
A stochastic numerical scheme for SDEs with fBm under non-Lipschitz
coefficient
Minoo Kamrani, m.kamrani@razi.ac.ir
Razi university, Islamic Republic of Iran
Our aim is to propose a numerical method for the solution of stochastic differential equa-
tions(SDEs) with fractional Brownian motion(fBM) which the diffusion coefficient is non-
Lipschitz. We consider fractional Brownian motions with Hurst parameter 1 < H < 1.
2
The basic idea is to apply Lamperti transformation to obtain a stochastic differential equa-
tion with additive noise. The well-posedness of this equation is proved and by applying a
numerical method which is based on Euler scheme, the solution of the transformed equation is
derived. Therefore, by using the inverse of the Lamperti transformation, numerical solution of
the main SDE is established.
Based on the properties of the Malliavin calculus, convergence of the proposed method is
explained. Furthermore the strong rate of convergence is derived.
A numerical solution to a nonlinear boundary value problem for the
Fredholm integro-differential equation
Sandugash Mynbayeva, mynbaevast80@gmail.com
Institute of mathematics and mathematical modeling, Kazakhstan
It is considered the boundary value problem (BVP) for the Fredholm IDE
dx m T t ∈ (0, T ), x ∈ Rn,
= f (t, x) + ϕk(t) ψk(τ )x(τ )dτ, (1)
dt
k=1 0
g [x(0), x(T )] = 0, (2)
where f : [0, T ] × Rn → Rn and g : Rn × Rn → Rn are continuous; the n × n matrices ϕk(t),
ψk(τ ), k = 1, m, are continuous on [0, T ], x = max |xi|.
i=1,n
651
