On a class of finite-difference schemes for solving ill-posed Cauchy problems in Banach spaces
Copyright policy )On a class of finite-difference schemes for solving ill-posed Cauchy problems in Banach spaces
Summary: A class of finite-difference schemes for solving ill-posed Cauchy problems for first-order linear differential equations with sectorial operators in Banach spaces is examined. Under various assumptions concerning the desired solution, time-uniform accuracy and error characteristics are obtained that refine and improve known estimates for these schemes. Some numerical results are presented.
- Mari State University Russian Federation
- Russian Academy of Sciences Russian Federation
Cauchy problem, convergence rate, Banach space, Iterative procedures involving nonlinear operators, Numerical solutions of ill-posed problems in abstract spaces; regularization, accuracy, Nonlinear ill-posed problems, regulating operator, first-order linear differential equations, finite difference scheme, ill-posed Cauchy problems
Cauchy problem, convergence rate, Banach space, Iterative procedures involving nonlinear operators, Numerical solutions of ill-posed problems in abstract spaces; regularization, accuracy, Nonlinear ill-posed problems, regulating operator, first-order linear differential equations, finite difference scheme, ill-posed Cauchy problems
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