es MNIBIO 21gen25 part I correzione

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* Questo modulo registrerà il tuo nome, inserire il nome. 21/1/2025 - MATHEMATICAL AND NUMERICAL METHODS IN ENGINEERING - NUMERICAL PART Prof. C. Vergara TIME : 1h 45' Rispondere direttamente su Forms o su un foglio di carta in base alle istruzioni indicate punto per punto. Per le risposte della parte 3 (scritte su un foglio di carta), consegnarle direttamente al docente ------------------------------------------------------------------------------------------------------------------------------- -- Respond directly on Forms or on a sheet of paper according to the step-by-step instructions. For answers of part 3 (written on a sheet of paper), please give them to the teacher Part I Quiz Answer the following questions: U^{n+1} = U^n + beta*dt/(2h)*B*U^n - dt*F^n U^{n+1} = U^n - beta*dt/(2h)*B*U^n + dt*F^n B*U^{n+1} = U^n - beta*dt/(2h)*U^n + dt*F^n (I+beta*dt/2h)*B)*U^{n+1} = U^n dt*F^n Given the matrix B with 0 on the main diagonal, +1 on the up main diagonal (elements (j,j+1)) and -1 on the low main diagonal (elemens (j,j-1)), and vectors F collecting approximation of the forcing terms/boundary conditions, which is the vectorial expression for the Forward Euler centered method applied to the unsteady advection problem with parameter beta? (1 punto) 1 It is not affected neither by numerical dissipation nor by numerical dispersion It is affected by a relevant numerical dissipation It is affected by a relevant numerical dispersion (i.e. a phase error) It is affected by relevant numerical dissipation and dispersion Which is true about the numerical solution obtained by means of the Lax-Wendroff scheme? (1 punto) 2 A diffusion/reaction partial differential equation A linear system with matrix A A system of ordinary differential equations with matrix A An ordinary…